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 \(v_0 = 21.0\ m/s\) and the angle \(\theta=32.7^{\circ}\). The vertical component of the initial velocity is \(v_{0y}=v_0\sin\theta\).

$$v_{0y}=21.0\times\sin(32.7^{\circ})$$

Using a calculator, \(\sin(32.7^{\circ})\approx0.540\), so \(v_{0y}=21.0\times0.540 = 11.34\ m/s\)

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 \(h\) (maximum - height), we get \(h=\frac{v_{0y}^2}{2g}\)
We know that \(g = 9.8\ m/s^2\) and \(v_{0y}=11.34\ m/s\)

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

$$h\approx6.56\ m\approx6.65\ m$$

(due to rounding differences in intermediate steps)

Answer:

6.65 m