Q.

A fighter plane enters inside the enemy territory at time t = 0, with velocity v0 = 250 m/s and moves horizontally with constant acceleration a = 20 m/s2 as shown in fig. (3).An enemy tank at the border, spot the plane and fires shots at an angle θ = 60o with the horizontal and with velocity u = 600 m/s. At what altitude H of the plane it can be hitted by the shot?

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a

15003m

b

125 m

c

1400 m

d

2473 m

answer is D.

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Detailed Solution

Let the fighter plane be hit at point Q.Suppose its horizontal distance is d as shown in fig. Now, d=v0t+12at2=(ucos⁡θ)t∴ t=ucos⁡θ−v0(a/2)=600×(1/2)−250(20/2)=5sFurther, H=(usin⁡θ)t−12gt2=(600×3/2)×5−12×10×25=15003−125=2473m
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