Question

A man is sitting on the shore of a river. He is in the line of 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 successful shot. Assume that the point of projection and the edge of the boat are in the same horizontal level.

Answer 1

The minimum and maximum angles of projection for successful shot is 15° to 18° or 71° to 75.

Explanation:

Step 1:

Given values  

x=5 m

speed = u=10 m/s

θ=?  

g=10 $m/s^2$

Step 2:

Minimum angle of projection:

x=5 m

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

$5=\frac{10^{2} \sin 2 \theta}{10}$

$5=\frac{100 \sin 2 \theta}{10}$

5=10 sin 2θ

$\sin 2 \theta=\frac{5}{10}$

$\sin 2 \theta=\frac{1}{2}$

$\sin 2 \theta=\frac{1}{2}=\sin 30^{\circ} \text { or } \sin 150^{\circ}$

θ=15° or 75°

Step 3:

Maximum angle of projection:

When x=6 m

$2 \theta=\sin ^{-1} \frac{g x}{u^{2}}$

$2 \theta=\sin ^{-1} \frac{10 \times 6}{10^{2}}$

$2 \theta=\sin ^{-1} \frac{10 \times 6}{100}$

$2 \theta=\sin ^{-1} \frac{6}{10}$

$2 \theta=\sin ^{-1} 0.6$

θ =18° or 71°

so for a successful shot , θ may vary from 15° to 18° or 71° to 75.

Answer 2

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