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  4. A shell fired from a gun at sea level rises to a maximum height of 5 km when fired at a ship 20 km away. The muzzle velocity should be

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Q. A shell fired from a gun at sea level rises to a maximum height of $ 5\, km $ when fired at a ship $ 20 \,km $ away. The muzzle velocity should be

AMUAMU 2015Motion in a Plane

Solution:

$H = 5000\,m = \frac{u_y^2}{2g} $
$ = \frac{u_y^2}{2\times 10}$
$u_y^2 = 100000 $
or $u_y = 100 \sqrt{10} \frac{m}{s}\,\,\,...(i)$
$R = 20, 000\,m = \frac{2u_x \,u_y}{g}$
$ = \frac{2\times u_x}{10} \times 100\sqrt{10}$
or $u_x = 100\sqrt{10}\,\,\,...(ii)$
Now, $ u = \sqrt{u_x^2 + u_y^2} $
$= 100\sqrt{20}\,m/s$