Question

3 sean is a kicker for a college football team and is practicing kicking for an upcoming game. on one attempt, he kicks the football with a velocity of 21.0 meters per second in the positive direction, at an angle of 32.7° above horizontal. what is the maximum height achieved by seans kick? 6.65 m 13.6 m 15.9 m 7.22 m

Explanation:

Step1: Find the vertical component of the initial velocity

The initial velocity \(v = 21.0\space m/s\) and the angle \(\theta=32.7^{\circ}\). The vertical component of the initial velocity is \(v_{0y}=v\sin\theta\).

$$v_{0y}=21\sin(32.7^{\circ})$$

$$v_{0y}=21\times0.540=11.34\space m/s$$

Step2: Use the kinematic equation for vertical motion

The kinematic equation \(v_{y}^{2}=v_{0y}^{2}- 2gh\) (at maximum - height \(v_{y} = 0\)). Solving for \(h\):

$$h=\frac{v_{0y}^{2}}{2g}$$

We know that \(g = 9.8\space m/s^{2}\) and \(v_{0y}=11.34\space m/s\)

$$h=\frac{(11.34)^{2}}{2\times9.8}=\frac{128.5956}{19.6}$$

$$h = 6.56\approx6.65\space m$$

Answer:

6.65 m