Question

Your annoying little brother is dropping rocks out of his bedroom window on the 2nd floor. You are on the ground floor and watch a rock fall past the patio door onto the ground below. In this problem, ignore air resistance. If the rock takes 0.30 s to cross the 2.5-m-high glass door, from what height above the top of the door was it dropped?

Answer 1

Let us consider the downwards direction as positive.

Gravitational acceleration = g = 9.81 m/s²

Initial velocity of the rock = V₁ = 0 m/s

Distance from where the rock is dropped to the top of the door = H₁

Velocity of the rock at the top of the door = V₂

Height of the glass door = H₂ = 2.5 m

Time taken by the rock to cross the door = T₂ = 0.3 sec

H₂ = V₂T₂ + gT₂²/2

2.5 = V₂(0.3) + (9.81)(0.3)²/2

V₂ = 6.86 m/s

V₂² = V₁² + 2gH₁

(6.86)² = (0)² + 2(9.81)H₁

H₁ = 2.4 m

Height of the drop from the top of the door = 2.4 m