First slide

Projectile motion

Question

An aeroplane moves with a horizontal velocity U at a height h. It drops a bomb. Then the time taken by the bomb in reaching the ground will be equal to

Easy

A

${(\frac{2 g}{h})}^{\frac{1}{2}}$
B

${(\frac{2 h}{g})}^{\frac{1}{2}}$
C

${(\frac{h}{2 g})}^{\frac{1}{2}}$
D

${(\frac{4 h}{g})}^{\frac{1}{2}}$

Solution

$b o m b v e l o c i t y h a s, i n i t i a l v e l o c i t y h o r i z o n t a l c o m p o n e n t = u_{x} = v e l o c i t y o f a e r o p l a n e i n i t i a l v e l o c i t y v e r t i c a l c o m p o n e n t = u_{y} = 0 a p p l y i n s_{y} = u_{y} t + \frac{1}{2} g t^{2} h e r e s_{y} = h e i g h t o f p l a n e f r o m g r o u n d = h; s u b s t i t u t e i n t h e e q u a t i o n, h = \frac{1}{2} g t^{2} t = \sqrt{\frac{2 h}{g}}$

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