Question

A plane is flying horizontally at a height of 1500 metre with velocity 200 metre per second passes directly

Answer 1

Answer:

Height of the fighter plane = 1.5 km = 1500 m

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

Let θ 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 = uxt

Distance travelled by the plane = vt

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

uxt = 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.

∴ H = u2Sin2 (90 – θ) / 2g

= (600)2 Cos2 θ / 2g

= 360000 X Cos2 19.5 / 2 X 10

= 16006.482 m

≈ 16 km