An airplane flying at a height of $1960 m$ from the ground with constant horizontal velocity of $600 km/h$ releases a bomb to hit a target on the ground. The time of flight and range of the bomb respectively are

15 s and 2.50 km

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20 s and 3.33 km

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25 s and 6.00 km

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20 s and 5.00 km

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Solution

The correct option is B $20 s and 3.33 km$

$u = 600 k m / h H = 1960 m$
$t_{f} =$ time of flight and
$R =$ range of projectile

Using, $H = u_{y} t_{f} + \frac{1}{2} g t_{f}^{2}$
$H = 0. t_{f} + \frac{1}{2} g t_{f}^{2}$
$\Rightarrow t_{f} = \sqrt{\frac{2 H}{g}}$
$t_{f} = \sqrt{\frac{2 \times 1960}{9.8}} = \sqrt{400} = 20 s$

Here, $R = u_{x} \times t_{f} = 600 \times \frac{20}{3600} k m$
$R = 10 / 3 k m \Rightarrow R = 3.33 k m$

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