Calculating the Speed of a Falling Ball

A student drops a ball from a window 3.5 m above the sidewalk. How fast is the ball moving when it hits the ground?

There are two ways to solve this problem:

First: Use the position equation

x = (1/2)at^2 + Vo*t + Xo

Where:

• Xo, the initial position, is 3.5 m
• X, the final position, is 0 m (the ground)
• Vo, the initial velocity, is 0 m/s (since the ball is dropped)
• a is -9.8 m/s^2

Substitute the values:

0 = (1/2)(-9.8)t^2 + 3.5

-3.5 = -4.9t^2

t^2 = 0.71

t ≈ 0.845 s

So, it takes the ball approximately 0.845 s to hit the ground.

Now, using the velocity equation:

v = at + Vo

v = (-9.8)(0.845) + 0

v ≈ -8.28 m/s

Therefore, the speed of the ball is approximately 8.28 m/s when it hits the ground.

Final answer: The ball will be moving at a speed of approximately 8.23 m/s when it hits the ground.

Explanation: To determine the speed of the ball when it hits the ground, we can use the equation:

v = gt

Question:

How fast is the ball moving when it hits the ground?

Answer:

The ball will be moving at a speed of approximately 8.23 m/s when it hits the ground.