A Tennis Ball Is Dropped From 120M Above The Ground?

A tennis ball is dropped from 120m above the ground. What is the speed of the tennis ball when it hits the ground?

Introduction

In this lab, you will be investigating what happens to a tennis ball when it is dropped from a height of 120m above the ground. You will be using your data to calculate the ball’s velocity at impact and to determine whether the ball bounced or not.

The Science

Every object has what is called terminal velocity, which is the constant speed that it falls at when the forces of air resistance and gravity are equal. The heavier the object, the higher its terminal velocity will be. When a tennis ball is dropped from 120m above the ground, it reaches a terminal velocity of around 53 m/s.

The Height

The height of the ball can be found using the following equation:

h = -5t^2 + 120

h is the height of the ball (in meters), t is the time (in seconds), and -5 is the acceleration due to gravity (in m/s^2).

So, if we plug in t = 10 (seconds), we get:

h = -5(10)^2 + 120
h = -500 + 120
h = 20 meters

The Velocity

In order to calculate the velocity of the tennis ball, we need to know two things: the height from which it was dropped, and the time it took to hit the ground.

The height is easy to find – it’s simply 120 meters. The time, however, is a bit more tricky. We can’t just measure how long it takes for the ball to hit the ground, because that would give us the time *elapsed* – that is, the time *since* the ball was dropped. We need to find the *time difference* – that is, how long it took *from when* the ball was dropped until *after* it hit the ground.

We can do this by using a stopwatch or a similar timing device. Start the timer when you release the ball, and stop it when it hits the ground. The difference between these two times – start time and stop time – is equal to the time taken for the ball to fall.

Now that we have both our pieces of information – height and time – we can plug them into our formula for velocity:

velocity = height / time

So in this case:

velocity = 120m / time (where ‘time’ is equal to our measured time difference)

The Math

A tennis ball is dropped from 120m above the ground. The ball falls for 3.5 seconds before it hits the ground. How long was the ball in the air? How fast was it going when it hit the ground?

The Formula

The formula for a projectile motion problem is:

y = y0 + v0yt + 1/2gt^2

where:

y is the final height of the projectile (in meters)
y0 is the initial height of the projectile (in meters)
v0 is the initial velocity of the projectile (in meters/second)
t is the time of flight (in seconds)
g is the acceleration due to gravity (in meters/second^2)

The Calculation

If we let 𝑎 be the acceleration due to gravity, then the formula for the height 𝑦 of the ball at any time 𝑡 seconds after it is dropped is:

𝑦=120−1 2𝑎𝑡2

We can use this formula to calculate how long it takes for the ball to reach the ground. We know that when 𝑦=0, the ball is at the ground, so we can set 𝑦=0 in our formula and solve for 𝑡:

0=120−1 2𝑎𝑡2
1 2𝑎𝑡2=120
⟹√(1 2𝑎(120))=√(1 2×9.8(120))≈11.17 seconds

The Conclusion

Assuming there is no air resistance, the tennis ball will reach a maximum height of 120 meters. At this point, the ball’s potential energy will be entirely converted to kinetic energy, and it will begin to fall back down to the ground. The ball will continue to accelerate as it falls, reaching a velocity of around terminal velocity before hitting the ground.