Question

Two stones are thrown vertically upwards simultaneously with their initial velocities u₁ and u₂ respectively. Prove that the heights reached by them would be in the ratio of u₁ ² : u₂ ² ( Assume upward acceleration is –g and downward acceleration to be +g ).

Answer 1

we know that v² - u² = 2as

or

for stone 1

v₁² - u₁² = 2as₁

or

s₁ = (v₁² - u₁²) / 2a = u₁² / 2g

similarly for stone 2

s₂ = u₂² / 2g

so, the ratio of the heights would be

s₁ / s₂ = (u₁² / 2g) / (u₂² / 2g)

or

s₁ / s₂ = (u₁² / u₂²) or s₁ : s₂ = u₁² : u₂²