4.30 A fighter plane flying horizontally at an altitude of 1.5 km with a speed 720 km/h passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed 600 m s-1 to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit? (Take g = 10 m s-2 ).

 

NEETprep Answer:

Heightoftheplane=1.5km=1500m
Speedoftheplane=720km/h=200m/s
Letθbetheanglewiththeverticalasshowninthefigure.

 

 

                         

Muzzle velocity of the gun, u = 600 m/s

Time taken by the shell to hit the plane = t

Horizontal distance travelled by the shell = ut

Distance travelled by the plane = vt

The shell hits the plane. Hence, these two distances must be equal.usinθ=vsinθ=vu=200600=13=θ.33θ=sin1(0.33)=19.5

In order to avoid being hit by the shell, the pilot must fly the plane at an altitude (H) higher than the maximum height achieved by the shell.

H=u2sin290-θ2g
=6002cos2θ2g
=360000xcos219.52x10
=18000x0.9432
=16006.482m
=16km