A particle of mass m is projected from the ground with initial linear momentum p (magnitude) to have maximum possible range. Its minimum kinetic energy will be

Question

A particle of mass m is projected from the ground with initial linear momentum p (magnitude) to have maximum possible range. Its minimum kinetic energy will be, p ⁡ 2 2 m ⁡, p ⁡ 2 4 m ⁡, p ⁡ 2 m ⁡, p ⁡ 2 3 m ⁡

MARKS App · Accepted Answer

At the time of projection θ = 4 5 o and momentum p ⁡ = m ⁡ u ⁡ ⇒ u = p m Minimum KE will be when projectile is at the highest point. Velocity will be is u cos θ ∴ K ⁡ min = 1 2 m ⁡ u cos θ 2 = m ⁡ 2 p ⁡ 2 m ⁡ 2 1 2 = p ⁡ 2 4m ⁡

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