Free Fall Worksheet

Question

Mr. P Throws a ball in the air releasing it 156 cm above the ground. If it hits the ground 2.34 s later, what was it’s maximum height? (with all steps included)

Answer 1

The three basic kinematics equations that you might need for this question are:

v = v₀ + at

y = y₀ + v₀t + 1/2 at²

v² = v₀² + 2a(y-y₀)

 

This notation may not be what you're used to. v₀ and y₀ represent the initial conditions of velocity and position. In free fall conditions, a = -g = -9.8 m/s².

 

In order to find the maximum height, you'll need to know the initial velocity. To do that, you use the information given about when it lands.

 

From the problem stated, you know that the ball lands on the ground when:

t = 2.34 s

y₀ = 1.56 m

y = 0 m (on the ground)

a = -9.8 m/s²

 

You can use the second equation to find v₀. The first and third equations require both the initial and final velocities, and you don't know either, so you can't use them.

y = y₀ + v₀t + 1/2 at²

0 = 1.56 + v₀ (2.34) + 1/2 (-9.8) (2.34)²

You can solve this for v₀.

 

At the top of its flight, the ball stops briefly at the maximum height.

v = 0

v0 from the previous step
y₀ = 1.56m

a = -9.8 m/s²

You want to find y. The third equation has all of these variables in it, so you can use it to solve for y.

 

v² = v₀² + 2a(y-y₀)

0² = (v₀)² + 2 (-9.8)(y - 1.56)

 

Plug in the value you found for v₀ earlier, and now you can solve for y.