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Question #42049

Difficulty: 8/10 | 🟢 Free

The Question

A small ball is dropped from a height $H = 20 \text{ m}$ above a large, horizontal platform initially at rest. The ball collides with the platform and rebounds with a coefficient of restitution $e = 0.5$ . An automated sensor detects the impact and, after a reaction time delay $\Delta t = 0.5 \text{ s}$ , causes the platform to accelerate vertically upwards with a constant acceleration $a = 4 \text{ m/s}^2$ . Assuming the platform's movement does not interfere with the ball before $\Delta t$ , what is the maximum height of the ball relative to the platform during its first rebound? (Take $g = 10 \text{ m/s}^2$ and neglect air resistance).

Options

A.
$\frac{65}{14} \text{ m}$
B.
$\frac{25}{7} \text{ m}$
C.
$\frac{235}{14} \text{ m}$
D.
5 \text{ m}

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

The Reaction Time Gap|Coefficient of Restitution|Mechanical Energy Conservation

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to couple a discontinuous collision event with a time-delayed, non-inertial reference frame.

The primary trap is the 'Reaction Time Gap': students frequently ignore the time shift in the platform's kinematic equation, incorrectly writing $y_p = \frac{1}{2}at^2$ instead of $\frac{1}{2}a(t - \Delta t)^2$ , which assumes the platform's acceleration begins at the exact instant of impact.

A secondary trap involves failing to apply the coefficient of restitution, confusing the pre-impact and post-impact velocities when setting up the relative motion equations.

The problem forces the rigorous application of time-shifted integration bounds and relative kinematics.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Straight Line - Class 11 Part 1
Concept	The Reaction Time Gap
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free