A 3.0 g spider is dangling at the end of a silk thread. You can make the spider bounce up and down on the thread by tapping lightly on his feet with a pencil. You soon discover that you can give the spider the largest amplitude on his little bungee cord if you tap exactly once every second. What is the spring constant of the silk thread?

a) The speed of the 60 Kg ball is  4.1 m/s

b) The KE before and after collision is  144 J and 64 J respectively

c) The KE lost is 80 J

We know that when we talk about the momentum, our minds would go to the collision of the objects that we have in this case which are the balls in the question.

a) Momentum before collision = Momentum after Collison

(2 * 12) + (4 * 60) = (8 * 2) + (60 * v)

v is the velocity of the 60Kg ball

24 + 240 = 16 + 60v

v = 4.1 m/s

b) KE before collision

1) 0.5 * 2 * (12)^2 = 144 J

2) 0.5 * 60 * 4^2 = 480 J

KE after collision;

1) 0.5 * 2 * 8^2 = 64 J

2) 0.5 * 60 * (4.1)^2 = 504.3 J

c) The KE lost in the collision is; 144 J - 64 J = 80 J

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If one could drive a Jetson's flying car at a constant speed of 160km/hr (100 mi/hr), the time it will take to drive around the Earth's equator is 250.47hours.

The time it will take to cover a certain distance can be calculated using the following formula;

Speed = distance ÷ time

According to this question, one could drive a Jetson's flying car at a constant speed of 160km/hr (100 mi/hr) across oceans and space. The distance around Earth at the Equator, its circumference, is 40,075 kilometers (24,901 miles).

Time = Distance ÷ speed

Time = 40,075km ÷ 160km/hr

Time = 250.47hours

Therefore, 250.47hours is the time it will take to cover around the Earth's equator.

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The change in the momentum is equal to the product of the mass and the change in the velocity.

what is change in momentum?

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If the value is positive, the member is in tension; otherwise, the member is in compression if the value is negative.

A force is an influence in physics that can change the motion of an object. A force can cause a mass object to change its velocity, or accelerate. Intuitively, force can be described as a push or a pull. A force is a vector quantity because it has both magnitude and direction. The term "force" has a specific meaning in science. At this level, it is perfectly acceptable to refer to a force as a push or a pull. A force is not something that an object possesses or possesses. Another object applies a force to another. The concept of a force is not restricted to living or non-living things.

Here,

If the value is positive, the member is in tension; if it is negative, the member is in compression.

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The magnitude of the n.et force on particle B due to the other two particles is  8 x 10¹⁹ N

The net force on particle B due to the other two particles is calculated by applying the formula for electric force.

F = ( kq₁q₂) / r²

where;

Electric force between A and B;

F(AB) = ( 9 x 10⁹ x 10 x 10⁻⁴ x 6.1 x 10⁴ ) / ( 0.73² )

F (AB) = 1.03  x 10¹² N

Electric force between B and C;

F(BC) = ( 9 x 10⁹ x 17.3 x 10⁴ x 6.1 x 10⁴ ) / ( 1.09² )

F (BC) = 8 x 10¹⁹ N

The net force on particle B is calculated as;

F (net) = - F (AB) - F (BC)

F (net) = - 1.03  x 10¹² N  -  8 x 10¹⁹ N

F (net) = -  8 x 10¹⁹ N

F (net) =  8 x 10¹⁹ N towards A

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C. 27 N force must be applied to lift the object.

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Answer: The angle at which the plane is flying relative to the tree is 19.47 degrees.

Explanation:

To calculate the angle at which the plane is flying relative to the tree, we can use the principle of trigonometry and the Pythagorean theorem. Since we know the distance from the plane to the nearest tree (60 meters), the height of the plane (10 meters), and the height of the tree (20 meters), we can use these measurements to form a right triangle with the plane, the tree, and the ground.

Using the Pythagorean theorem, we can calculate the length of the hypotenuse of the right triangle. The length of the hypotenuse is the distance between the plane and the top of the tree. The hypotenuse is calculated by the square root of (distance^2 + height of the plane^2 + height of the tree^2)

The angle we are trying to calculate is opposite to the height of the tree, therefore we can use the tangent function:

tan(angle) = opposite/adjacent

opposite = height of the tree = 20m

adjacent = distance = 60m

angle = arctan(20/60) = arctan(1/3) = 19.47122063449069 degrees

The angle at which the plane is flying relative to the tree is 19.47 degrees.

1. The net force is 79.1°

The angle between those two forces is 120 degrees (because the triangle is equilateral) so the net force on particle 3 is the vector sum of the two forces.

The direction of the force on particle 3 due to particle 1 is along the line joining particles 1 and 3. The direction of the force on particle 3 due to particle 2 is along the line joining particles 2 and 3.

To find the net electric force acting on particle 3 due to particles 1 and 2, we can use Coulomb's law, which states that the force between two point charges is given by the equation:

[tex]F = k * (q1 * q2) / r^2[/tex]

where F is the force, k is the Coulomb constant [tex](8.99 x 10^9 N * m^2/C^2)[/tex], q1 and q2 are the charges of the two particles, and r is the distance between the two particles.

In this case, we have three particles placed at the corners of an equilateral triangle, with a side length of 3.1 cm. Since the triangle is equilateral, all three sides are equal in length, so r1 = r2 = 3.1 cm

The net force on particle 3 is the vector sum of the two forces acting on it due to particles 1 and 2.

F3 = F31 + F32 where F31 is the force on particle 3 due to particle 1 and F32 is the force on particle 3 due to particle 2

[tex]F31 = k * (q3 * q1) / r1^2[/tex]

[tex]F32 = k * (q3 * q2) / r2^2[/tex]

[tex]F31 = 8.99 x 10^9 N * m^2/C^2 * (8.0 nC * -8.4 nC) / (3.1 cm)^2[/tex]

[tex]F32 = 8.99 x 10^9 N * m^2/C^2 * (8.0 nC * -16.8 nC) / (3.1 cm)^2[/tex]

[tex]F31 = -9.52 * 10^{-4 N}[/tex]

[tex]F32 = -1.93 * 10^{-3 N}[/tex]

[tex]F3 = F31 + F32 = -2.88 * 10^{-3 N}[/tex]

After solving, The net force = 79.1°

The direction of the force on particle 3 due to particle 1 is along the line joining particles 1 and 3. The direction of the force on particle 3 due to particle 2 is along the line joining particles 2 and 3.

The angle between those two forces is 120 degrees (because the triangle is equilateral) so the net force on particle 3 is the vector sum of the two forces

2. Particle 3 will move in the direction of the net force acting on it, which is the vector sum of the two forces acting on it due to particles 1 and 2.

Since the net force is [tex]-2.88 * 10^{-3 N}[/tex], and the angle between the direction of the forces on particle 3 due to particles 1 and 2 is 120 degrees, particle 3 will move in the direction of the angle bisector of the angle between those two forces.

The angle bisector of 120 degrees is 60 degrees, thus the net force is acting on particle 3 at 60 degrees with respect to the positive x-axis.

The instant after being released, particle 3 will move in the direction of the net force vector and it will have a velocity vector pointing in the same direction as the net force.

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The answer is B. 2 s. The impulse provided by both engines is the same, so they must fire for the same amount of time in order to provide that amount of impulse.

Engines are devices that convert energy into mechanical force, usually to power machines and vehicles. Engines come in a variety of forms and sizes, but all are based on the same basic principles of converting thermal energy into mechanical force via combustion.

Since the first engine fires for 2 s and provides 6 N of thrust,
the second engine must also fire for 2 s to provide 4 N of thrust (since 6N/2s = 4N/x, where x = 2s).

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The magnitude of the charge on each bead is 7.08nc.

Given the following information:

Original length = 4.0 cm converted to m = 0.04 m

1.4 grams to kilograms = 0.0014

5.1 cm to m = 0.051 is the new length.

4.6 cm to m = 0.046 m is the final length.

e =  0.051 - 0.046

= 0.005m in length

Scientific evidence:

Gravitational acceleration = 9.8m/s²

Coulomb's constant is equal to 8.99 x 10⁹ Nm²/C²

We would use Coulomb's law to calculate the magnitude of the charge (in nC) on each bead:

First, we would calculate the spring constant of this lightweight spring

using the following formula:

W = mg = Ke

K = mg/e

K = 0.014 x 9.8 / 0.05

K = 2.744N/m

K, the spring constant, is 2.744N/m.

In terms of electrostatic force:

F = ke

F = 2.77 x 0.05

F = 0.1385

F equals 0.1385 Newton.

Coulomb's electrostatic force law.

The charge in an electric field can be calculated mathematically using the following formula:

q = √F/k x r

We get by substituting the given parameters into the formula;

q = √(0.1385/8.99 x 10⁹) x 0.046

q = √(1.54060 x 10⁻¹²) x 0.046

q = 7.08 x 10⁻⁸

Take note that 1 nC = 1 x 10⁻⁹ C

Charge, q = 7.08nc

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When an Olympic track runner begins at rest and has an acceleration of 1.6 m/s2 for 3.7 seconds, then has zero acceleration for the remainder of the race, the runner's speed at time t is 2.08 m/s.

Velocity is a vector representation of an object's or particle's displacement with respect to time. The meter per second (m/s) is the standard unit of velocity magnitude (also known as speed). Alternatively, velocity magnitude can be expressed in centimeters per second (cm/s). The direction of movement of the body or item is defined by velocity. Speed is fundamentally a scalar number. Velocity is, in essence, a vector quantity. It is the pace at which distance changes. It is the displacement rate of change. Speed is the pace at which an item moves along a route in time, whereas velocity is the rate and direction of movement. In other words, velocity is a vector, whereas speed is a scalar number.

Here,

put the values of Vi, a and t in first equation of motion

Vf = Vi + a×t

Vf = 0 + 1.6×1.3

Vf = 2.08 m/s

The runner's speed at time t as 1.3 seconds is 2.08 m/s when Olympic track runner starts from rest and has an acceleration of 1.6 m/s2 for 3.7 s, then has zero acceleration for the remainder of the race.

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When the accumulation of snow and ice during the winter months exceeds the ice melt during the summer months, the mass of a glacier increases.

The complete question:

"the mass of a glacier ____ when the accumulation of snow and ice during the winter months is larger than ice melt during summer months. fill in the blank with the best word choice from the list below.

a. increases

b. decreases."

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Option D: Apply a force of magnitude 2F for a period of time t=2T to a mass m object. The impulse will rise as the force, the passage of time, or the object's mass increase.

The force times the length of time that the force is applied to an item results in the impulse. For a force to impose an impulse on an item, both the force applied and the time period during which it is applied must be non-zero. The scenario in which a force of magnitude 2F is applied to an item of mass m over a period of time t = 2T results in option D being the right response. This is so that, since the impulse is computed as the product of force and time, the impulse will not change if the force and time are both doubled. Alternatives like A, B, and C wouldn't cause an impulse to be applied to an object.

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The kinetic energy at the lowest point is 1.96 Joule. The result is obtained by using the concept of Conservation of mechanical energy.

The Conservation of mechanical energy states that the total mechanical energy of a system is conserved. It can be expressed as

E initial = E final

KE₁ + U₁ = KE₂ + U₂

½mv₁ + mgh₁ = ½mv₂ + mgh₂

Where

The index 1 and 2 shows at point 1 (initial) and 2 (final).

A pendulum that consists of

At its lowest point, find kinetic energy!

The lowest point is at the mean position where h = 0.

Let's say, point 1 is at the highest point and point 2 is at the lowest point.

E initial = E final

½mv₁ + mgh₁ = ½mv₂ + mgh₂

At the highest, the speed is zero. h max means highest position. It would be

½m(0) + mgh₁ = ½mv₂ + mg(0)

mgh₁ = ½mv₂

U₁ = KE₂

The kinetic energy is

KE₂ = mgh₁

KE₂ = 2 (9.8) (0.1)

KE₂ = 1.96 Joule

Hence, the kinetic energy at the lowest point is 1.96 Joule.

The correct option is (G).

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The force applied by the ball on the wall is 3.994 Newton, if the mass of the ball is 58 gm, and initial velocity is 34 m/s.

Mass of the ball, m = 58 gm = 0.058 kg

Initial velocity of the ball, u = +34 m/s

Time of the applied force, t = 1 sec

Final velocity of the ball, after collision, v = -34 m/s  [negative: as the direction is opposite]

Let the force applied by the ball on the wall is F. We know the rate of change of momentum of an object is equal to the force applied by the object. So,

F = (m₁v₁ - m₂v₂)/t

F = (0.058 × 34 - 0.058(-34))

F = 3.944 N

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10.628 kW of power must the winch motor provides when the car is moving at constant speed at the slope of 30.0o at a speed of 2.20m/s for 12 s to keep of moving.

The maximum Force, with the maximum speed of the motor, gives maximum power Now we know

a = (vf-vi)/t = (2.20 - 0)/12 => 0.1853 m/s^2

The maximum force is when the car is accelerating so,

f = fa+fg

F = ma+ ma * sign 30o => 4831.035 N ( As  shown in the Image attached how the perpendicular vector that is a signθ is taken)

So the force will be 4831.035 N

Hence the maximum power p = fxV

4831.035 * 2.20

P =10626.27 w

which results in 10626.27/1000 kW

So 10.628 Kw is the maximum power required for the slop of 30o.

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The solution with the lowest total ion concentration, assuming full dissociation, is 2 M aluminum sulphate.

Concentration in chemistry is defined as the abundance of an ingredient divided by the total volume of a combination. There are four sorts of mathematical descriptions: mass concentration, molar concentration, number concentration, and volume concentration. The amount of a material, such as salt, that is present in a certain amount of tissue or liquid, such as blood. When there is less water present, a material becomes more concentrated. When a person does not drink enough water, the salt in his or her urine may become more concentrated. A substance's concentration is the amount of solute contained in a given amount of solution. Molarity is the number of moles of solute in one liter of solution and is used to express concentrations.

Here,

The solution with the lowest total ion concentration, assuming full dissociation, is 2 M aluminum sulfate.

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Due to Eugene's intense control, the emotional environment for mom, jaja, and kambili is very confined and controlled.

The children never laugh, speak up, truly experience childhood, or grin as a result of Papa's ways. Additionally, they are never permitted to make mistakes or be themselves. Papa is very severe because he did not have a lot growing up and wants his children to appreciate what they have. He is this way also because he virtually sees himself as a god and uses the bible to justify everything.

Eugene, the father, is incredibly controlling, which restricts and controls the emotional atmosphere for mom, jaja, and kambili. Due to papa's ways, the kids never speak up, laugh, or truly experience childhood. They also never smile. They're never let to make mistakes or be themselves, either. Papa is very severe because he did not have a lot growing up and wants his children to appreciate what they have. He too thinks this way; he uses the Bible to support all he does and almost considers himself to be divine.

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So the heat dacy can be calculated using the  winger way formula

In one day ,[tex]P_{d}(t)=\\[/tex][tex]6.65\times 10^{-3}[/tex] GW(t), In one month =[tex]P_{d}(t)=\\[/tex][tex]1.946\times 10^{-3}[/tex] GW(t) , in one year  ,  [tex]P_{d}(t)=\\[/tex][tex]2.29\times 10^{-4}[/tex] GW(t)

According to thermodynamics, heat is a type of energy that crosses a thermodynamic systems' boundary due to a temperature differential across the barrier Heat is absent in thermodynamic systems. However, the expression is also regularly used to describe the thermal energy that constitutes a system's internal energy and is reflected in the system's temperature. In all senses of the word, energy is a form of heat.

For the  decay we have winger way formula as ,

[tex]P_{d} =0.0622P_{0}[t-0.2-(t_{0}-0.2(t_{0}+t)-0.2][/tex]

[tex]P_{0}=1.5GW(t)[/tex],[tex]t_{0}=31,536,000[/tex]

[tex]P_{d}(t)=\\[/tex]thermal power generation due to beta and gamma rays

[tex]t_{0}=[/tex]time in seconds , of thermal power level before shut down

t= rime , in seconds elapsed since the shutdown

a)  In one day ,

Number of seconds ,t=86400s

so , P

[tex]P_{d}(t)=\\[/tex]0.0622 x 1.5 x [86,400-0.2-(31,536,000+86,400)-0.2]

[tex]P_{d}(t)=\\[/tex][tex]6.65\times 10^{-3}[/tex] GW(t)

b ) In one month

Number of seconds ,t=2629800s

[tex]P_{d}(t)=\\[/tex]0.0622 x 1.5 x [2629800-0.2-(31,536,000+2629800)-0.2]

[tex]P_{d}(t)=\\[/tex][tex]1.946\times 10^{-3}[/tex] GW(t)

c) In one year  

Number of seconds ,t=2629800s

[tex]P_{d}(t)=\\[/tex]0.0622 x 1.5 x [31,536,000-0.2-(15,768,000+31,536,000)-0.2]

[tex]P_{d}(t)=\\[/tex][tex]2.29\times 10^{-4}[/tex] GW(t)

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The line 1-0+t2 in relation to the plane x-2y+z =1 is parallel to the plane as both points satisfy the plane equation.

A plane is a two-dimensional, Euclidean surface which never ends in the mathematics. A plane is a point's (zero dimensions), a line's (one dimensions), and space's (three dimensions) two-dimensional equivalents.

A line is a network of interconnected points that can go on forever in both the directions. Three noncollinear points, two parallel lines, or two intersecting lines can all be used to form a plane. If two points are on the same line, they are said to be collinear.

The question is incomplete, find the complete question here

which of the following is true about the line 1-0+t2 in relation to the plane x-2y+z =1 ? group of answer choices

the line lies on the plane.

the line intersects the plane in one point.

the line is parallel to the plane.

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Answer:

Temperature

Explanation:

Commonly when speaking about the temperature outside we will refer to it as --degrees Fahrenheit or Celsius. So if I were to tell my friend that it is currently 68 degrees outside, that would mean that the current temperature is 68 degrees Fahrenheit or Celsius outside.

-Hope this helped

The internal torque acting at point C is 800 lb-ft clockwise, and at point D is  1500 ft-lb anti-clockwise.

The shaft is bearing at a and b. As the shaft is at rest and not rotating in any direction. So the internal torque must be balancing the external torques acting on the shaft. Near the bearing A, the the external torque acting on the shaft is 1500 lb-ft clockwise, so at point D there must be an anti-clockwise torque. So the torque acting on the D is 1500 ft-lb.

Similarly, near the bearing B the external torque acting on the shaft is 800 lb-ft anti-clockwise, so there must be an equal and external clockwise torque working on point C to balance the 800 anti-clockwise torque. So the internal torque working on point C is 800 lb-ft.

--The given question is incomplete, the complete question is:

"the support bearings at a and b allow free turning of the shaft. (figure 1) figure1 of 1 part a determine the resultant internal torque acting on the cross section at points c and d . enter your answers in newton-meters to three significant figures separated by a comma."

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The resistance of working potential difference of the 6.2 V, 4.5 W lamp is 8.54 ohm. When terminal pd across the battery is 6.2 V, the emf of the battery is 8.01 V.

The opposition that a substance provides to the flow of electric current is referred to as resistance. The uppercase letter R represents it. The ohm is the standard unit of resistance, which is sometimes written as a word and sometimes represented by the uppercase Greek letter omega. Resistance is a measure of an electrical circuit's resistance to current flow. Resistance is measured in ohms, which is represented by the Greek letter omega ().

Here,

r=2.5 ohm

V= 6.2 volts

P=4.5 watt

P=V²/R

R=V²/P

R=6.2*6.2/4.5

R=8.54 ohm that is about 9 ohm.

I=V/R

I=0.726 A

EMF=V+Ir

=6.2+0.726*2.5

=6.20+1.81

=8.01 volts

The resistance of the 6.2 V, 4.5 W lamp at its working potential difference is 8.54 ohm. The emf of the battery when terminal pd across the battery is 6.2 V is 8.01 V.

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When a person or business avoids paying their tax responsibilities, it is a criminal violation that entails fines and penalties.

If Chloe doesn't pay her overdue taxes, then Internal Revenue Service will impose penalties. The threat is removed after she makes a payment. Now, she will finish her work more swiftly. This illustrates the application of behavior control.

On the contrary hand, tax avoidance is entirely legal. Qualified taxpayers may claim a variety of deductions, credits, or income adjustments in accordance with IRS regulations. For instance, some homeowners are permitted to write off the interest they pay off their mortgage.

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(1) The total pressure of the pipe at point 1 is 1.85 x 10⁵ Pa.

(2) The total pressure of the pipe at point 2 is  146,950 Pa.

The total pressure at position 1 and 2 is calculated by applying Bernoulli's equation as shown below.

P (t) = P₀ + ρgh

where;

The total pressure of the pipe at point 1 is calculated as follows;

P (t) = ( 1.85 x 10⁵ )  +   ( 1000 x 9.8 x 0 )

P (t) = 1.85 x 10⁵ Pa

The total pressure of the pipe at point 2 is calculated as follows;

P (t) = ( 1.2 x 10⁵ ) + ( 1000 x 9.8 x 2.75 )

P (t) = 146,950 Pa

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The complete question is below:

Water flows through a pipe as shown in the figure. The pressure at points 1 and 2 respectively is 1.85 x 10ª Pa and 1.20 x105 Pa. The

radius of the pipe at points 1 and 2 respectively is 3.30 cm and 1.40 cm. If the vertical distance between points 1 and 2 is 2.75 m, determine

the following.

(1) the total pressure at point 1

(2) the total pressure at point 2

During Stanford University's "Search for Isolated Fractionally Charged Particles," more than 100 million more oil droplets were measured, hence option A is correct.

Theoretically, every charge must be a multiple of the charge of an elementary particle or an electron.

Similar automated equipment to that of Millikan and Fletcher was employed. No droplet with a fractional charge was discovered.

Therefore, even if the quantity used today for the elementary charge differs slightly from what Millikan and Fletcher measured, it is generally agreed that all charge is made up of multiples of the elementary charge.

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When a softball is thrown from an 80-meter-high building at a velocity of 10 meters per second, the height after t seconds is 148 feet.

Velocity is a vector representation of an object's or particle's displacement with respect to time. The meter per second (m/s) is the standard unit of velocity magnitude (also known as speed). Alternatively, velocity magnitude can be expressed in centimeters per second (cm/s). The direction of movement of the body or item is defined by velocity. Speed is fundamentally a scalar number. Velocity is, in essence, a vector quantity. It is the pace at which distance changes. It is the displacement rate of change. Speed is the pace at which an item moves along a route in time, whereas velocity is the rate and direction of movement. In other words, velocity is a vector, whereas speed is a scalar number.

Here,

The maximum height the ball will reach is the vertex of the parabola s(t)=48+80t-16t2. first, we need to solve for t. The vertex of any parabola of the form f(x)=ax2+bx+c is found by using x=-b/2a. In this case, x=t, b=80 and a=-16. Substituting we get:

]t=-80/((2)(-16)--->t=-80/-32--->t=5/2

Putting this value of t in the original formula will give us the maximum height:

s(t)=48+80t-16t2

s(5/2)=48+80(5/2)-16(5/2)2

s(5/2)=48+200-16(25/4)

s(5/2)=248-100

smax=148 feet

It's height, in meters, after t seconds is 148 feet when softball is thrown off of a building that is 80 meters high at a velocity of 10 meters per second.

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The propositions P and Q are both true. P states that you can paddle one canoe down the river, and Q states that you can paddle one kayak down the river. Both of these activities are possible, making both statements true.

A proposition is a statement or assertion that expresses a judgment or opinion about a particular topic or issue. It is a type of argument used in logic and critical thinking, and is typically expressed in a declarative sentence. Propositions can be either true or false and can be used to support or reject a claim. In philosophy, propositions can also be used to explain and justify a particular belief or set of beliefs. Propositions are often used in academic and scientific discourse to communicate ideas and arguments in a concise and logical manner.

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The correct statement is:

"The magnitude of the acceleration of object A is 6 times less than the magnitude of the acceleration of object B"

The magnitude of the acceleration for an object can be calculated using Coulomb's law, which states that the force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. The formula for the force between two charges is:

F = (k * q1 * q2) / r^2

where F is the force, k is the Coulomb constant, q1 and q2 are the charges, and r is the distance between the charges.

Since the acceleration is the force divided by the mass, we can use the formula:

a = F / m

where a is the acceleration, F is the force, and m is the mass.

Given that the charge on object A is 3 times higher than on object B, and object A has a 6 times higher mass than object B, we can determine that:

The force acting on object A is 3 times greater than the force acting on object B (due to the difference in charges)

The mass of object A is 6 times greater than the mass of object B

So, the acceleration of object A is 6 times less than the acceleration of object B.

Therefore, the correct statement is:

"The magnitude of the acceleration of object A is 6 times less than the magnitude of the acceleration of object B"

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The angle θ between P and Q vector is 18.43°.

In physics, a vector is a quantity that has both magnitude and direction. It is typically represented by an arrow with the same direction as the quantity and a length proportional to the magnitude of the quantity.

A vector, while having magnitude and direction, does not have position. A vector quantity is any physical quantity that has both directions and magnitude.

According to given parameters:

PQ sinθ = (1/3) PQ cosθ

tanθ = 1/3

θ = 18.43°

Hence, the angle θ between P and Q vector is 18.43°

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