Question

1. a machine launches a tennis ball at an angle. the ball has an initial vertical velocity of 9.0 m/s and an initial horizontal velocity of 9.0 m/s.

a). find the total time the ball spends in the air. (hint: find the times from vertical direction).
b). find the total horizontal distance the ball travels.

Explanation:

Step1: Find time to reach maximum height

Use the formula $v = v_i+at$ in vertical - direction. At maximum height, $v = 0$, $v_{iy}=9.0$ m/s and $a=-g=- 9.8$ m/s².
$0 = 9.0-9.8t_{up}$
$t_{up}=\frac{9.0}{9.8}\text{ s}$

Step2: Calculate total time in air

The time to go up is equal to the time to come down. So $t_{total}=2t_{up}$.
$t_{total}=2\times\frac{9.0}{9.8}\approx1.84$ s

Step3: Find horizontal distance

In the horizontal direction, $a_x = 0$, $v_{ix}=9.0$ m/s and we use the formula $d = v_{ix}t$.
$d=9.0\times1.84 = 16.56$ m

Answer:

a. $t_{total}\approx1.84$ s
b. $d = 16.56$ m