Answer to Question #113991 in Classical Mechanics for Arshid Ali

Question

Pam is playing football and is about to take a penalty. She kicks the ball at an angle of 60°
and with initial velocity 18.5 m/s.
a) What is the maximum height the ball will reach?
b) If she is 30 metres from the goal will the ball enter the goal?

Answer 1

(a) the maximum height the ball reaches

$$H_{\rm max}=\frac{(v_0\sin\theta)^2}{2g}$$ $$=\frac{(18.5\sin60\degree)^2}{2\times 9.8}=13.1\:\rm m$$

(b) the vertical position of the ball

$$y=x\tan\theta-\frac{gx^2}{2(v_0\cos\theta)^2}$$

$$=30\tan 60\degree-\frac{9.8\times 30^2}{2(18.5\cos 60\degree)^2}=0.42 \:\rm m$$