Question

A plane flying horizontally at a height of 1500 m with a velocity of $200m{s}^{-1}$ passes directly overhead an antiaircraft gun. Then the angle with the horizontal at which the gun should be fired for the shell with a muzzle velocity of 400 $m{s}^{-1}$ to hit the plane is:

• A. ${90}^{\circ }$
• B. ${60}^{\circ }$
• C. ${30}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is B ${60}^{\circ }$

Velocity of plane $v_p=200m/s$, velocity of bullet $v_b=400m/s$,

For the shell to hit the plane, horizontal velocity of shell = horizontal velocity of the plane because initial horizontal displacement between plane and shell is zero.

$h=1500m;\theta =?$
$400cos\theta =200$
$cos\theta =\frac{1}{2}$
$\theta ={60}^0$
Hence option B is correct.