Question:

Two stones are thrown up simultaneously from the edge of a cliff $240\, m$ high with initial speed of $10\, m/s$ and $40\, m/s$ respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first? (Assume stones do not rebound after hitting the ground and neglect air resistance, take $g=10\, m/s^2$)

Updated On: Sep 27, 2024
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The Correct Option is C

Solution and Explanation

$I\,st$ stone
$0 \leq t \leq 8$ sec
$v_{r}=40-10$
$=30 \,m / s$
$a_{r}=0$

$s_{r}=v_{r} \times t=30 \times 8=240\, m$

$8$ sec $< t \leq 12$ sec
$v _{ r }$ increases in magnitude and relative acceleration is $g$ downwards


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Concepts Used:

Motion in a straight line

The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion. 

Types of Linear Motion:

Linear motion is also known as the Rectilinear Motion which are of two types:

  1. Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
  2. Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.