Question

A fighter plane flying horizontally passes over an antiaircraft gun with a uniform velocity 200 ms^-1. The gun can fire the shell with a velocity $200 \sqrt{2} {ms}^{- 1}$ . At what angle should the gun fire the shell so as to hit the plane?

Moderate

Solution

Let velocity of shell = U and velocity of plane = V and $θ$ be the angle at which shall is fired to hit the plane, then
$\begin{array}{l} Ucos θ = V \Rightarrow \cos θ = \frac{V}{U} = \frac{200}{200 \sqrt{2}} \\ \cos θ = \frac{1}{\sqrt{2}} \Rightarrow θ = 45^{\circ} \end{array}$

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