JEE Main · 2023 · 29 Jan 2023 · Shift 1 · Kinematics

A stone is projected at angle

3 0^{\circ}

to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be :

(A) $1 : 2$
(B) $1 : 4$
(C) $4 : 1$
(D) $4 : 3$ ✓ Correct

Answer: (D)

Solution

At launch the stone has speed

u

, so its kinetic energy is

\frac{1}{2} m u^{2}

. At the top only the horizontal part

u cos 3 0^{\circ}

survives, giving kinetic energy

\frac{1}{2} m (u cos 3 0^{\circ})^{2}

. The ratio is

\frac{1}{cos ^{2} 3 0 ^{\circ}} = \frac{1}{3/4}

. The kinetic energy at projection to that at the highest point is

4 : 3

JEE Main · 2023 · 29 Jan 2023 · Shift 1 · Single correct option

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