Answer to Question #113991 in Classical Mechanics for Arshid Ali

Question #113991
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?
1
Expert's answer
2020-05-05T18:41:16-0400

(a) the maximum height the ball reaches


Hmax=(v0sinθ)22gH_{\rm max}=\frac{(v_0\sin\theta)^2}{2g}=(18.5sin60°)22×9.8=13.1m=\frac{(18.5\sin60\degree)^2}{2\times 9.8}=13.1\:\rm m

(b) the vertical position of the ball


y=xtanθgx22(v0cosθ)2y=x\tan\theta-\frac{gx^2}{2(v_0\cos\theta)^2}

=30tan60°9.8×3022(18.5cos60°)2=0.42m=30\tan 60\degree-\frac{9.8\times 30^2}{2(18.5\cos 60\degree)^2}=0.42 \:\rm m

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