First slide

Projectile motion

Question

Three stones A, B and C are simultaneously projected from same point with same speed. A is thrown upwards, B is thrown horizontally and C is thrown downwards from a building. When the distance between stone A and C becomes 10 m, then distance between A and B will be

Difficult

A

10 m
B

5 m
C

$5 \sqrt{2} m$
D

$10 \sqrt{2} m$

Solution

Let the stones be projected at t = 0 sec with a speed z from point O. Then an observer, at rest at t = 0 and having constant acceleration equal to acceleration due to gravity, shall observe the three stones move with constant velocity as shown. In the given time each ball shall travel a distance 5 metre as seen by this observer. Hence the required distance between A and B will be
$= \sqrt{5^{2} + 5^{2}} = 5 \sqrt{2} metre$

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