A fighter plane flying horizontally at an altitude of $$1.5$$ km with speed $$720$$ km $$h-l$$ 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 $$s-l$$ to hit the plane. (Take$$ g: $$l0$$ m $$s-2)

Question

A fighter plane flying horizontally at an altitude of $$1.5$$ km with speed $$720$$ km $$h-l$$ 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 $$s-l$$ to hit the plane. (Take$$ g: $$l0$$ m $$s-2)

Infinity Learn · Accepted Answer

Here,Speed of the plane, v $$=$$ $$720$$ km $$h-1$$    $$=$$ $$720$$ × $$518$$ $$ms-1$$ $$=$$ $$200$$ $$ms-1Speed$$ of the shell, u $$=$$ $$600$$ $$ms-1Let$$ the shell will hit the plane at L after time t if fired at an angle θ with the vertical from O.For hitting, horizontal distance travelled by the plane $$=$$ horizontal distance travelled by the shell.i.e., v ×t $$=$$ u $$sin$$ θ ×t    $$sin$$ θ $$=$$ $$vu=$$ $$200$$ $$ms-1600$$ $$ms-1$$ $$=$$ $$13$$     θ $$=$$ $$sin$$$$-1(13)$$

A fighter plane flying horizontally at an altitude of 1.5 km with speed 720 $km h^{- l}$ 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 $s^{- l}$ to hit the plane. (Take g: l0 m $s^{- 2}$ )

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A fighter plane flying horizontally at an altitude of 1.5 km with speed 720 km h-l 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-l to hit the plane. (Take g: l0 m s-2)

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A fighter plane flying horizontally at an altitude of 1.5 km with speed 720 $km h^{- l}$ 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 $s^{- l}$ to hit the plane. (Take g: l0 m $s^{- 2}$ )