Question

A cannon of mass $5$m (including a shell of mass m) is at rest on a smooth horizontal ground, fires the shell with its barrel at an angle $\theta$ with the horizontal at a velocity u relative to cannon. Find the horizontal distance of the point where shell strikes the ground from the initial position of the cannon.

• A. $\frac{16u^2\sin 2\theta }{9g}$
• B. $\frac{u^2\sin 2\theta }{5g}$
• C. $\frac{3u^2\sin 2\theta }{5g}$
• D. $\frac{8u^2\sin 2\theta }{5g}$

Answer 1

The correct option is A $\frac{16u^2\sin 2\theta }{9g}$

Initial momentum is zero, as it is in rest.

Let recoil velocity be v.

u is the velocity relative to canon.

From conservation of momentum,'4mv= m(u+v)

4v=u+v

v= u/3

Hence initial velocity= (u+v)=u+ (u/3)

=4u/3

Angle of projection =$\theta$

Range= $\frac{u^{2}Sin2\theta }{g}$

$\frac{{16u}^{2}Sin2\theta }{9g}$