Question

A man is siting on the shore of a river. He is in the line of a 1.0 m long boat and is 5.5 m away from the centre of the boat. He wishes to throw an apple into the boat. If he can throw the apple only with a speed of 10 m/s, find the minimum and maximum angles of projection for seccessful shot. Assume that the point of projection and the edge of the boat are in the same horizontal level.

Answer 1

When the apple just touches the end B of the boat.

x = 5 m, u = 10 m/s,$\theta$ = ?, g = 10 $m/s^2$

x = $\frac{u^{2}sin2\theta }{g}$

$\Rightarrow 5=\frac{(10{)}^{2}sin2\theta }{10}=10sin2\theta$

$\Rightarrow Sin2\theta =\frac{1}{2}=sin{30}^{0}orsin{150}^0$

$\Rightarrow \theta ={15}^{0}or{75}^0$

Similary for end C, x = 6 m

Then 29 = $si{n}^{-1}\left(\frac{gx}{u^2}\right)$

= $sin-1\left(0.6\right)={18}^{0}or{71}^0$

So, for a successful shot, $\theta$ may vary from ${15}^{0}to{18}^{0}or{71}^{0}to{75}^0$