A jet aeroplane is flying at a constant height of 2 km with a speed 360 ${kmh}^{- 1}$ above the ground towards a
target and releases a bomb. After how much time, it will hit the target and what will be the horizontal
distance of the aeroplane from the target, so that the bomb should hit the target? (Take, 9 = 10 ${ms}^{- 1}$ )

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40 s, 4 km

30 s, 3 km

10 s, 1 km

20 s, 2 km

answer is B.

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Detailed Solution

Given, $H = 2000 m, u = 360 {kmh}^{- 1}$

$u = 360 \times \frac{5}{18} = 100 {ms}^{- 1}$

The time taken by the bomb to hit the target is

$T = \sqrt{\frac{2 H}{g}} = \sqrt{\frac{2 \times 2000}{10}} = 20 s$

The horizontal distance of the aeroplane from the target,

$R = u \sqrt{\frac{2 H}{g}} = 100 \times 20 = 2000 m = 2 km$

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