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.