xavier throws a tennis ball to his friend olaf at a 20° angle relative to the ground with an initial…

xavier throws a tennis ball to his friend olaf at a 20° angle relative to the ground with an initial velocity of 18 m/s. the tennis ball travels 30 m until olaf catches it. the time the tennis ball was in the air, rounded to the nearest hundredth, is s.

xavier throws a tennis ball to his friend olaf at a 20° angle relative to the ground with an initial velocity of 18 m/s. the tennis ball travels 30 m until olaf catches it. the time the tennis ball was in the air, rounded to the nearest hundredth, is s.

Answer

Explanation:

Step1: Resolve initial velocity into components

The initial velocity in the x - direction $v_{0x}=v_0\cos\theta$ and in the y - direction $v_{0y}=v_0\sin\theta$, where $v_0 = 18$ m/s and $\theta = 20^{\circ}$. $v_{0x}=18\cos(20^{\circ})\approx18\times0.9397 = 16.9146$ m/s, $v_{0y}=18\sin(20^{\circ})\approx18\times0.3420 = 6.156$ m/s.

Step2: Find the time of flight using horizontal motion

In horizontal motion (no acceleration, $a_x = 0$), the horizontal displacement $x = v_{0x}t$. We know $x = 30$ m and $v_{0x}\approx16.9146$ m/s. We can solve for $t$ from the formula $t=\frac{x}{v_{0x}}$. $t=\frac{30}{16.9146}\approx1.77$ s.

Answer:

$1.77$