Question

A cannon is to fire up to $500m$ horizontally. What should be the angle of projection, if the shells are fired with a velocity of $100m/s$? $(g=10m/s^2)$

Answer 1

Given $V=100ms$ and Range $R=500m$ and $g=10m/s^2$

Let the angle of projection is $\theta$ with the horizontal.

Horizontal velocity $V_H=Vcos\theta =100cos\theta$

Vertical velocity $V_V=Vsin\theta =100sin\theta$

$\therefore$ Time of flight $=\frac{2V_V}{g}=\frac{2\times 100sin\theta }{g}$

$\Rightarrow$ Range $=V_H\times \text{Time of flight}$

$\Rightarrow \frac{100cos\theta \times 2\times 100sin\theta }{g}=500$ $\Rightarrow sin2\theta =\frac{1}{2}$

$\Rightarrow 2\theta ={30}^o$ $\Rightarrow \theta ={15}^o$