A body is thrown from ground vertically upwards into an...

A body is thrown from ground vertically upwards into an empty tank of height $\mathrm{H}$ in minimum time. The tank is now filled with water so that the acceleration inside is reduced to $\frac{\mathrm{g}}{2}$. The height h from which the body should be thrown so that the time is unchanged is (a) $0.5 \mathrm{H}$ (b) $0.66 \mathrm{H}$ (c) $0.8 \mathrm{H}$ (d) $0.9 \mathrm{H}$

A body is thrown from ground vertically upwards into an empty tank of height $\mathrm{H}$ in minimum time. The tank is now filled with water so that the acceleration inside is reduced to $\frac{\mathrm{g}}{2}$. The height h from which the body should be thrown so that the time is unchanged is
(a) $0.5 \mathrm{H}$
(b) $0.66 \mathrm{H}$
(c) $0.8 \mathrm{H}$
(d) $0.9 \mathrm{H}$

Key Concepts

Effect of Medium on Acceleration

When a projectile moves through different media, the effective acceleration acting on it may change due to additional forces such as drag or buoyancy. In this problem, the filling of the tank with water reduces the acceleration to g/2, and understanding this effect is crucial for analyzing how the projectile’s motion, particularly its time of flight, is altered.

Time Optimization

Time optimization in kinematics involves determining parameters (such as the initial velocity or starting height) that minimize or equalize the travel time of a projectile. In this context, the problem requires adjusting the release height so that the total time of flight remains unchanged even when the acceleration is reduced.

Projectile Motion

This concept involves the study of objects moving under the influence of gravity only, following a curved path. The problem examines vertical motion where the object is projected upward, and the standard kinematics equations are used to calculate displacement, velocity, and time under uniform acceleration.

Uniformly Accelerated Motion

This key concept refers to motion in which the acceleration remains constant throughout the movement. The kinematic equations, such as s = ut + 1/2at², are used to analyze the motion of the body both in free space (with acceleration g) and within the water (with a reduced acceleration of g/2).

Please give Ace some feedback