Question:
A ball $A$ is thrown up vertically with a speed $u$ and at the same instant another ball $B$ is released from a height $h$. At time $t$, the speed of $A$ relative to $B$ is
A ball $A$ is thrown up vertically with a speed $u$ and at the same instant another ball $B$ is released from a height $h$. At time $t$, the speed of $A$ relative to $B$ is
Updated On: Jun 7, 2024
- $ u $
- $ 2u $
- $ u-gt $
- $ \sqrt{({{u}^{2}}-gt)} $
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The Correct Option is A
Solution and Explanation
From equation of motion,
we have $ v=u+gt $
where u is initial velocity and t is time.
For ball A, $ {{v}_{A}}=u-gt $
For ball B, $ {{v}_{B}}=0+gt $
$ \therefore $ Relative speed, $ \Delta \overrightarrow{v}={{\overrightarrow{v}}_{A}}-{{\overrightarrow{v}}_{B}} $
$ =(u-gt)\hat{j}-(-gt\,\hat{j}) $
$ =u\hat{j} $
we have $ v=u+gt $
where u is initial velocity and t is time.
For ball A, $ {{v}_{A}}=u-gt $
For ball B, $ {{v}_{B}}=0+gt $
$ \therefore $ Relative speed, $ \Delta \overrightarrow{v}={{\overrightarrow{v}}_{A}}-{{\overrightarrow{v}}_{B}} $
$ =(u-gt)\hat{j}-(-gt\,\hat{j}) $
$ =u\hat{j} $
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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.