Question

# Two bodies A and B are thrown simultaneously. A is projected vertically upwards with 20 m/s speed from the ground and B is projected vertically downwards from a height of 40 m at the same speed and along the same line of motion. At what point do the two bodies collide? (g=10 m/s2)

A
10 m from ground
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B
15 m from ground
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C
20 m from ground
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D
25 m from ground
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Solution

## The correct option is B 15 m from groundConsidering upward direction to be positive For A Initial velocity u=20 m/s Acceleration aA=−g Initial displacement (xA)i=0 m (considering the ground to be origin) For B Initial velocity u=−20 m/s Acceleration aB=−g Initial displacement (xB)i=40 m (considering the ground to be origin) Now, considering motion of A w.r.t. B Initial velocity of A w.r.t. B=uAB=uA−uB=(20)−(−20) =40 m/s Acceleration of A w.r.t. B=aAB=aA−aB=0 Using second equation of motion, SAB=uABt+12aABt2 ⇒40=40t ⇒t=1 s Displacement of A with respect to ground, SA=20×1−12×10×12=15 m ∴ The two bodies will collide at a height of 15 m from the ground.

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