Question

1. gabriel kicks a soccer ball so that it has an initial velocity 22 meters per second, at an angle of 16° above the ground. how much time does it take for the soccer ball to reach its maximum height? 0.62 s 2.16 s 0.77 s 2.24 s

Explanation:

Step1: Find the vertical component of initial velocity

The initial velocity \(v = 22\space m/s\) and the angle \(\theta=16^{\circ}\). The vertical component of the initial velocity is \(v_y=v\sin\theta\).

$$v_y = 22\times\sin(16^{\circ})$$

$$v_y=22\times0.2756\approx6.0632\space m/s$$

Step2: Use the kinematic equation \(v = v_0+at\) to find the time to reach maximum height

At maximum height, the vertical velocity \(v = 0\). The acceleration due to gravity \(a=-g=- 9.8\space m/s^{2}\) (negative because it acts in the opposite direction of motion).
Using the equation \(v = v_y+at\), we solve for \(t\).

$$0 = 6.0632-9.8t$$

$$9.8t=6.0632$$

$$t=\frac{6.0632}{9.8}\approx0.62\space s$$

Answer:

0.62 s