A shot travelling at the rate of 100 ms^–1 is just able to pierce a plank 4 cm thick. What velocity is required to just pierce a plank 9 cm thick? 

Here, v₁ = 100 m/s, s₁ = 4 cm; v₂ = ?, s₂ = 9 cm.

As the kinetic energy of the shot is spent in doing work against plank resistance F,

¹/₂ m v₁² = F × s₁

and

¹/₂ m v₂² = F × s₂

Dividing, we get:

v₂² / v₁² = s₂ / s₁

⇒ v₂ / v₁ = √(s₂ / s₁) = √(9 / 4) = 3 / 2

∴ v₂ = (3 / 2) × v₁ = (3 / 2) × 100 = 150 m/s