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. $16\frac{u^{2}sin2\theta }{9g}$
• 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 $16\frac{u^{2}sin2\theta }{9g}$

since initial momentum is 0 final must also be,
relative $=u$
hence absolute $=u+v..$.where $v=$recoil velocity,

$4m.v=m(u+v)$

$v=\frac{u}{3}$

hence initial velocity$=u+\frac{u}{3}=\frac{4u}{3}$
and angle of projection$=A$
hence Rang= $16\frac{u^{2}sin2\theta }{9g}$