A tennis ball is thrown straight up with an initial speed of 20.0 m/s. It is caught at the same distance above the ground. How high does the ball rise (m), and how long does the ball stay in the air (s)?
20.41 meters
4.08 seconds
no answer
To determine the height the ball rises and the time it stays in the air, we need to use the equations of motion for vertical motion.
Let's break down the problem step by step:
Step 1: Identify the known values:
- Initial speed (v₀) = 20.0 m/s (upward)
- Final speed (v) = 0 m/s (at the highest point, when the ball changes direction)
- Acceleration (a) = -9.8 m/s² (acceleration due to gravity, acting downward)
Step 2: Find the time it takes for the ball to reach its highest point:
We can use the equation of motion: v = v₀ + at, where t is the time taken.
0 = 20.0 + (-9.8)t
9.8t = 20.0
t = 20.0 / 9.8
t ≈ 2.04 seconds
It takes approximately 2.04 seconds for the ball to reach its highest point.
Step 3: Find the height the ball rises:
To find the maximum height, we need to use the equation of motion: Δy = v₀t + (1/2)at², where Δy represents the change in height.
Δy = (20.0)(2.04) + 0.5(-9.8)(2.04)²
Δy = 40.8 - 20.08
Δy ≈ 20.72 meters
The ball rises to a height of approximately 20.72 meters.
Step 4: Find the total time the ball stays in the air:
The time the ball stays in the air is twice the time it takes to reach the highest point since the time going up is equal to the time coming down.
Total time = 2t
Total time = 2 * 2.04
Total time ≈ 4.08 seconds
The ball stays in the air for approximately 4.08 seconds.
To summarize:
- The ball rises to a height of approximately 20.72 meters.
- The ball stays in the air for approximately 4.08 seconds.