﻿ A fighter plane flying horizontally at an altitude of 1.5 km with 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 to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit? (Take g = 10 m/s2) from Physics Motion in A Plane Class 11 Manipur Board

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A fighter plane flying horizontally at an altitude of 1.5 km with 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 to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit? (Take g = 10 m/s2)

Velocity of shell is, u  = 600 m/s

Velocity of fighter plane is, v = 720 km/hr = 200 m/s

Let the shell be fired at angle θ with vertical.

To hit the fighter plane, the horizontal component of muzzle speed should be equal to the velocity of plane.

i.e.

The maximum height attained by the shell is,

That is,

Therefore the minimum altitude for safe flight is 16km.

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