Question

a ball is thrown vertically upwards upward with a speed of 20.0 m/s and its caught again at the same level. how long is the ball in the air?

Explanation:

Step1: Determine the time to reach the maximum height

Use the formula \(v = v_0+at\). At maximum height, \(v = 0\). The acceleration \(a=-g=- 9.8\ m/s^{2}\), and \(v_0 = 20.0\ m/s\).

$$0=20 - 9.8t$$

$$t=\frac{20}{9.8}\ s$$

Step2: Calculate the total time of flight

The time to go up is the same as the time to come down. So the total time \(T = 2t\).

$$T=2\times\frac{20}{9.8}$$

$$T=\frac{40}{9.8}\approx4.08\ s$$

Answer:

The ball is in the air for approximately \(4.08\ s\)