4.30 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^-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 ).

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Vishal Baghel | Contributor-Level 10

5 months ago

4.30

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

The altitude of the plane = 1.5 km =1500 m

Velocity of the shell = 600 m/s

$\sin ? θ$ = 200/600

$∴ θ = 19.47 °$

Let H be the minimum altitude for the plane to fly, without being hit

Using equation H = $u^{2}$ sin2 (90- $θ) / 2 g$

= (6002cos2 $θ$ )/2g

= 360000 { ( 1 + cos2 $θ$ )/2}/2 $\times$ 10

= 16000 m = 16 km

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