Figure shows two inclined planes. A ball released from height h falls on to the left plane and is reflected from it. After four perfectly elastic collisions on the planes the ball arrives at the initial starting point. Find the time elapsed between start and arrival if α = 30° and h = 5 m.

Engineering

Physics

Straight Line Motion

Collision

Projectile Motion

Question

Figure shows two inclined planes. A ball released from height h falls on to the left plane and is reflected from it. After four perfectly elastic collisions on the planes the ball arrives at the initial starting point. Find the time elapsed between start and arrival if α = 30° and h = 5 m.

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T = 2t₁ + 2t₂ + 2t₃

$t_{1} = t_{3} = \sqrt{\frac{2 h}{g}} = 1 \sec$

$t_{2} = \frac{2 \times \sqrt{2 gh} \sin 30^{\circ}}{g} = 1 \sec$

T = 2 + 2 + 2 = 6 sec.