Question:
A stone thrown vertically upwards with a speed of 5 m/sec attains a height $H_1$. Another stone thrown upwards from the same point with a speed of 10 m/sec attains a height $H_2$. The correct relation between $H_1$ and $H_2$ is
A stone thrown vertically upwards with a speed of 5 m/sec attains a height $H_1$. Another stone thrown upwards from the same point with a speed of 10 m/sec attains a height $H_2$. The correct relation between $H_1$ and $H_2$ is
Updated On: Jul 6, 2022
- $H_2 = 4 H_1$
- $H_2 = 3 H_1$
- $H_1 = 2 H_2$
- $H_1 = H_2$
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The Correct Option is A
Solution and Explanation
From third equation of motion $v^2 = u^2 + 2ah $
In first case initial velocity $u_1 = 5 \, m/ \sec$
final velocity $v_1 = 0, a = - g$
and max. height obtained is $H_1$, then,
$H_1 = \frac{25}{2g}$
In second case $u_2 = 10 \, m/ \sec, v_2 = 0, a = -g$
and max. height is $H_2$ then, $H_2 = \frac{100}{2g}$
It implies that $H_2 = 4H_1$
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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.