Question

A man is sitting on the shore of a river. He is in the line of a $1.0m$ long boat and is $5.5m$ 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 $10m/s$, find the minimum and maximum angles of a projection for successful shot. Assume that the point of projection and the adge of the boat are in the same horizontal level.

Answer 1

Given that,

$R=5.5m$

$g=10m/s^2$

$u=10m/s$

Now, the minimum angle of projection

Take the range is

$R_{min}=5.5-1$

$R_{min}=4.5m$

Then,

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

$4.5=\frac{{\left(10\right)}^2\times \sin 2\theta }{9.8}$

$\sin 2\theta =\frac{4.5\times 9.8}{100}$

$2\theta ={26.16}^0$

$\theta ={13}^0$

Now, the maximum angle of projection

Take the range is

$R_{max}=5.5+1$

$R_{max}=6.5m$

Then,

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

$\sin 2\theta =\frac{6.5\times 9.8}{100}$

$2\theta ={39.56}^0$

$\theta ={19.8}^0$

$\theta ={20}^0$

Hence, the minimum angle of projection is ${13}^0$ and maximum angle of projection is ${20}^0$