Figure shows an elevator cabin, which is moving downwards with constant acceleration $a$ . A particle is projected from corner $A$ , directly towards diagonally opposite corner $C$ . Then prove that
a. Particle will hit $C$ only when $a = g$
b. Particle will hit the wall $C D$ if $a < g$
c. Particle will hit the roof $B C$ if $a > g$ .

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Solution

Superimpose an upward acceleration $a$ on the system.

The box becomes stationary. The particle has an upward acceleration $a$ and a downward acceleration $g$ .
If $a = g$ the particle has no acceleration and will hit $C$ .

if $a > g$ , the particle has no acceleration and if $a < g$ , the particle has a net downward acceleration.

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