Question:
From a building two balls $A$ and $B$ are thrown such that $A$ is thrown upwards and $B$ downwards (both vertically). If $v_{A}$ and $v_{B}$ are their respective velocities on reaching the ground, then :
From a building two balls $A$ and $B$ are thrown such that $A$ is thrown upwards and $B$ downwards (both vertically). If $v_{A}$ and $v_{B}$ are their respective velocities on reaching the ground, then :
Updated On: Jul 5, 2022
- $v_{B}>y_{A}$
- $v_{A}=v_{B}$
- $v_{A}>v_{B}$
- their velocities depend on their masses
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The Correct Option is B
Solution and Explanation
From conservation of energy, potential energy at height $h$ $= KE$ at ground Therefore, at height $h,$ PE of ball $A$
$PE =m_{A} g h$
$KE$ at ground $=\frac{1}{2} m_{A} v_{A}^{2}$
So, $m_{A} g h =\frac{1}{2} m_{A} v_{A}^{2}$
$v_{A} =\sqrt{2 g h}$
Similarly, $v_{B} =\sqrt{2 g h}$
Therefore, $ v_{A}=v_{B}$
: In question it is not mentioned that magnitude of thrown velocity of both balls are same which is assumed in solution.
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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:
- 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.
- 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.