A bullet of mass 200 g having initial kinetic energy 90 J is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to 40 J within 1 s, the minimum length of the pool, the bullet has to travel so that it completely comes to rest is

Solution

Physics sir · 4 steps

Find the constant water resistance from the first second, then see how far it takes to drain all 90 J.

1. Speeds from KE. With m = 0.2 kg, v = √(2K/m). So 90 J gives v₁ = √900 = 30 m s⁻¹, and 40 J gives v₂ = √400 = 20 m s⁻¹.
2. Retarding force. Take the water's resistance as constant. The speed drops by 10 m s⁻¹ in 1 s, so the retardation is a = 10 m s⁻². The resisting force is F = ma = 0.2 × 10 = 2 N.

   F d = Kᵢₙᵢₜᵢₐₗ - 0 ⇒ d = (90 J)/(2 N)

3. Work-energy theorem. The work done against this force must remove all 90 J of kinetic energy. As a check, v²/2a = 900/20 = 45 m gives the same distance.
4. So. The bullet travels 45 m before it comes to rest, so the pool must be at least 45 m long.

The idea to keep. When a constant force slows a body, the work-energy theorem gives the stopping distance directly: total KE divided by the resisting force. Find the force first from any piece of the motion you are given.

Answer from the NTA final answer key. Solution by PrepWiser.