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Home » A fighter plane flying horizontally at an altitude of 1.5 km with a speed of 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 ).
A fighter plane flying horizontally at an altitude of 1.5 km with a speed of 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 ).
CBSE | Class 11 | Motion in a Plane | NCERT | Physics
A fighter plane flying horizontally at an altitude of 1.5 km with a speed of 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 ).

Answer :

According to the question, speed of the fighter plane is 720 km/h

or, 720 x (5/18) = 200 m/s

Altitude of the plane is1.5 km and the velocity of the shell is 600 m/s

From the diagram above, we can write

sin θ = 200/600

sin θ = 1/3

Or, θ = sin-1 (1/3)

θ = 19.470

Suppose H is the minimum altitude then using the following equation,

H = u2 sin2 (90 – θ)/2g

Substituting values, we get => H = (6002 cos2θ)/2g

H = 6002 cos 2θ/(2 x 9.8)

H = {360000[(1+cos 2θ)/2]}/2g

H = 360000[1+cos2 (19.470)/2]/2g

H = 360000 [ (1 + 0.778)/2]/19.6

H = (360000 x 0.889) /19.6 = 320040/19.6

H = 16328 m

Therefore, H = 16.328 km

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