Question

A fighter plane flying horizontally with speed 200 m/s. The gun is fired when the plane is just above it. What should be the minimum height of the plane so as to avoid hitting by the shell? The velocity of the shell is 400 m/s.

Answer 1

Answer:

16km

Explanation:

Height of the fighter plane =1.5km=1500 m

Speed of the fighter plane, v=720km/h=200 m/s

Let be the angle with the vertical so that the shell hits the plane. The situation is shown in the given figure.

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 =u

x

t

Distance travelled by the plane =vt

The shell hits the plane. Hence, these two distances must be equal.

u

x

t=vt

u Sin θ=v

Sin θ=v/u

=200/600=1/3=0.33

θ=Sin −1 (0.33)=19.50

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 for any angle of launch.

H

mma =u 2 sin 2 (90−θ)/2g=600 2/(2×10)=16km