An aeroplane flies horizontally at height , h in a straight line at a constant speed , u . When it is directly above a cannon on the ground , the cannon fires a shell which is supposed to hit the airplane . Ignore the air resistance , determine in terms of u,g and h the minimum muzzle speed of the shell , v.

Firstly , i resolve the velocity into 2 parts (ie $\displaystyle v_x $ and $\displaystyle v_y$)

$\displaystyle

v_x=u\cos \theta\Rightarrow v^2_x=u^2\cos^2 \theta

$

$\displaystyle

v^2_y=u^2+2as

$

$\displaystyle =u^2\sin^2 \theta-2gh $

$\displaystyle v=\sqrt{v^2_x+v^2_y}$

$\displaystyle

=\sqrt{u^2-2gh}

$

The error here is in that sign , why should it be positive .