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  4. At the height 80 m, an aeroplane is moved with 150 m / s . A bomb is dropped from it, so as to hit a target. At what distance from the target should the bomb be dropped ? (g=10 m / s 2)

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Q. At the height $80\, m$, an aeroplane is moved with $150\, m / s . A$ bomb is dropped from it, so as to hit a target. At what distance from the target should the bomb be dropped ? $\left(g=10\, m / s ^{2}\right)$

Bihar CECEBihar CECE 2004Motion in a Straight Line

Solution:

Time taken by the bomb to reach the ground is given by
$h_{O A}=\frac{1}{2} g t_{O B}^{2}$
image
we have $t_{O B}=\sqrt{\frac{2 h_{Q A}}{g}}$
Given, $ h_{O A}=80 \,m , g =10\, m / s ^{2} $
$ \therefore t_{O B}=\sqrt{\frac{2 \times 80}{10}}=4 s$
Horizontal velocity of bomb $v=150\, m / s$
Horizontal distance covered by the bomb
$A B =v t_{O B}$
$=150 \times 4 $
$=600 \,m$
Hence, the bomb-should be dropped $600\, m$ before the target.