Free-Fall Motion (w/ a tennis ball)

In summary: You are given the initial height and the final height, so you can find the initial velocity and the final velocity by substitution into the first two equations. Then use the third equation to find the time. Then plug the velocities and the time into the fourth equation.In summary, the conversation discusses testing the quality of a tennis ball by dropping it from a height of 4.00m and measuring its rebound height of 2.00m. The question asks for the average acceleration during the ball's contact with the floor, which can be found by using equations of motion with constant acceleration. The conversation also includes a mistake in the calculations, which can be corrected by using the equations s=ut+\frac{1}{2}at^2
  • #1
Feldoh
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3

Homework Statement


To test the quality of a tennis ball, you drop it onto the floor from a height of 4.00m. It rebounds to a height of 2.00m. If the ball is in contact with the floor for 12.0ms, (a) what is the magnitude of its average acceleration during that contact and (b) is the average acceleration up or down?

Homework Equations


Equations of motion w/ constant acceleration

The Attempt at a Solution


I'm pretty sure (b) is up for starters since the ball reaches a height of 2m after it is on the ground which means it's got to accelerate up.

My problem is with part a. I started by figuring out the velocity of the ball the moment it hits the ground.

[tex]v = at[/tex]

[tex]v = \frac{y-y_o}{t}[/tex]

So substituting the second equation in the first one and solving for t:
[tex]t = \sqrt{\frac{y-y_o}{a}}[/tex]

[tex]t = \sqrt{\frac{-4m}{-9.80\frac{m}{s^s}}} = .64s[/tex]

Since I got the time...

[tex]v = v_{o}+at = 0 + (-9.80)(0.64) = -6.3m/s[/tex]

In my mind I thought that I had the initial velocity of the time interval it was on the ground and I thought that the final velocity would be 0 since if it was greater than 0 the ball would be traveling "up".

First I found the time in s and got 12.0ms = .012s, then:
[tex]a_{avg} = \frac{v-v_o}{t} = \frac{0-(-6.3)}{.012}[/tex]

My answer was a = 525m/s^2, but it's wrong -- my book says its 1.26*10^3 m/s^2

So uhh... where did I go wrong? XD
 
Last edited:
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  • #2
Oh don't think it would really matter at all in this problem but assume there is no air resistance.
 
  • #3
How did you get the time? Try using [tex]s=ut+\frac{1}{2}at^2[/tex] and [tex]s=vt-\frac{1}{2}at^2[/tex]. Then applying [tex] v=\frac{y_1-y_o}{t}[/tex], find the velocity just before it hits and just after it rebounds, use [tex] a=\frac{(v-u)}{t_o}[/tex], remembering that one velocity vector points downward and the other vector points upward.
 
  • #4
bel said:
How did you get the time? Try using [tex]s=ut+\frac{1}{2}at^2[/tex] and [tex]s=vt-\frac{1}{2}at^2[/tex]. Then applying [tex] v=\frac{y_1-y_o}{t}[/tex], find the velocity just before it hits and just after it rebounds, use [tex] a=\frac{(v-u)}{t_o}[/tex], remembering that one velocity vector points downward and the other vector points upward.

Whoops should have made it a bit clearer how I derived the time. I edited my first post.

But I really don't get what your saying to do...
 
  • #5
Well, get two different veocities, by the first three equations, and use the fourth to find your acceleration.
 

FAQ: Free-Fall Motion (w/ a tennis ball)

1. What is free-fall motion?

Free-fall motion is the motion of an object falling under the influence of gravity alone, with no other forces acting upon it. It is characterized by a constant acceleration towards the ground, known as the acceleration due to gravity.

2. How does free-fall motion differ from other types of motion?

Unlike other types of motion, free-fall motion does not involve any external forces, such as air resistance or friction, acting on the object. The only force acting on the object is the force of gravity.

3. What factors affect the free-fall motion of a tennis ball?

The main factor that affects the free-fall motion of a tennis ball is the acceleration due to gravity, which is determined by the mass of the Earth and the distance from the tennis ball to the center of the Earth. Other factors that may have a small impact include air resistance and the shape and size of the tennis ball.

4. How can we calculate the acceleration due to gravity using a tennis ball?

The acceleration due to gravity can be calculated using the equation a = g = F/m, where F is the force of gravity and m is the mass of the tennis ball. By measuring the time it takes for the tennis ball to fall a certain distance and using the formula d = ½gt2, we can solve for the acceleration due to gravity.

5. Can free-fall motion occur in other environments besides Earth?

Yes, free-fall motion can occur in any environment where there is a force of gravity acting on an object. For example, free-fall motion can also occur on the moon or other planets with a gravitational pull. However, the acceleration due to gravity may vary in these environments due to differences in mass and distance from the object to the center of gravity.

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