Question

A man is siting on the shore of a river , He is in the line of a $1.0m$ long beat 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 spped of $10m/s$, 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

When the applekust touches the end $B$ of the boat$x=5m,u=10m/s,g=10m/s^2,\theta =?$$x=\frac{u^2\sin 2\theta }{g}$$\Rightarrow S=\frac{{10}^2\sin 2\theta }{10}\Rightarrow S=10\sin 2\theta$$\Rightarrow \sin ={15}^o$ or ${75}^o$Simmilarly for end $C,x=6m$Then $2{\theta }_1={\sin }^{-1}\left(gx/u^2\right)={\sin }^{-1}\left(0.6\right)={182}^o$ or ${71}^o$.So, for a successful shot, $\theta$ may very from${15}^o$ to ${18}^o$ or ${71}^o$ to ${75}^o$