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 = 60^o with the horizontal and with velocity u = 600 m/s. At what altitude H of the plane it can be hitted by the shot?

Question

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 = 60^o with the horizontal and with velocity u = 600 m/s. At what altitude H of the plane it can be hitted by the shot?

Infinity Learn · Accepted Answer

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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