A paratrooper jumps from a height H. The parachute can provide a uniform deceleration of 2 m s

step 1 Let H1 is equal to height of free fall, height of free fall before parachute opens. Also H2 is e

A paratrooper jumps from a height H. The parachute can...

A paratrooper jumps from a height $\mathrm{H}$. The parachute can provide a uniform deceleration of $2 \mathrm{~m} \mathrm{~s}^{-2}$. The height above the ground at which the parachute should be opened so that he touches ground with zero speed is $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$ (a) $\frac{\mathrm{H}}{6}$ (b) $\frac{4 \mathrm{H}}{5}$ (c) $\frac{5 \mathrm{H}}{6}$ (d) $\frac{6 \mathrm{H}}{7}$

A paratrooper jumps from a height $\mathrm{H}$. The parachute can provide a uniform deceleration of $2 \mathrm{~m} \mathrm{~s}^{-2}$. The height above the ground at which the parachute should be opened so that he touches ground with zero speed is $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) $\frac{\mathrm{H}}{6}$
(b) $\frac{4 \mathrm{H}}{5}$
(c) $\frac{5 \mathrm{H}}{6}$
(d) $\frac{6 \mathrm{H}}{7}$

Key Concepts

Uniformly Accelerated Motion

This concept involves the study of bodies moving under a constant acceleration. The fundamental kinematic equations, such as v = u + at and s = ut + 0.5at^2, allow us to relate displacement, velocity, acceleration, and time in scenarios where acceleration is uniform. These equations apply whether the acceleration is positive (speeding up) or negative (slowing down).

Free Fall

Free fall refers to the motion of an object solely under the influence of gravity, with no other forces acting on it, assuming air resistance is negligible. During free fall, the object accelerates downwards at a constant rate (g), which simplifies its analysis using the equations of uniformly accelerated motion.

Deceleration

Deceleration is a specific case of uniform acceleration where the acceleration opposes the direction of motion, thereby reducing the speed of an object. In problems involving deceleration, the kinematic equations are used with a negative acceleration value to determine the distance required to bring an object to rest.

Segmented Motion Analysis

In many real-life problems, including ones involving changes in acceleration, the motion is divided into different segments or phases. Each segment (such as free fall before parachute deployment and decelerated descent after deployment) is analyzed separately using appropriate kinematic equations, and the results are linked using continuity conditions like matching final and initial velocities at the point of transition.

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