Question

3 a tennis ball is launched horizontally at a speed of 24.4 meters per second, and at a height of 2.10 meters above the ground. how long will it take for the tennis ball to reach the ground? 0.654 s 0.551 s 5.06 s 2.49 s

Explanation:

Step1: Analyze the vertical motion

The tennis ball is in free - fall vertically. The initial vertical velocity \(v_{0y}=0\ m/s\), the vertical displacement \(y = 2.10\ m\), and the acceleration due to gravity \(g = 9.8\ m/s^{2}\). The equation for vertical displacement in free - fall is \(y=v_{0y}t+\frac{1}{2}gt^{2}\). Since \(v_{0y} = 0\ m/s\), the equation simplifies to \(y=\frac{1}{2}gt^{2}\).

Step2: Solve for time \(t\)

From \(y=\frac{1}{2}gt^{2}\), we can solve for \(t\). Rearranging the formula gives \(t=\sqrt{\frac{2y}{g}}\).
Substitute \(y = 2.10\ m\) and \(g = 9.8\ m/s^{2}\) into the formula:

$$t=\sqrt{\frac{2\times2.10}{9.8}}=\sqrt{\frac{4.2}{9.8}}\approx\sqrt{0.4286}\approx0.654\ s$$

Answer:

0.654 s