Question:
A body is projected vertically upwards. The times corresponding to height $h$ while ascending and while descending are $t_1$ and $t_2$ respectively. Then the velocity of projection is ($g$ is acceleration due to gravity).
A body is projected vertically upwards. The times corresponding to height $h$ while ascending and while descending are $t_1$ and $t_2$ respectively. Then the velocity of projection is ($g$ is acceleration due to gravity).
Updated On: Feb 23, 2024
- $g \sqrt {t_1 t_2}$
- $\frac {gt_1t_2}{t_1+t_2}$
- $\frac {\sqrt{gt_1t_2}} {2}$
- $\frac {g(t_1 + t_2)}{2} $
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The Correct Option is D
Solution and Explanation
In case of motion under gravity, time taken to go up is equal to the time taken to fall down through the same distance.
Time of descent $\left(t_{2}\right)=$ time of ascent $\left(t_{1}\right)=\frac{u}{g}$
$\therefore$ Total time of flight $\quad T=t_{1}+t_{2}=\frac{2 u}{g}$
$\Rightarrow\,\,\,\,\,\,u=\frac{g\left(t_{1}+t_{2}\right)}{2}$
Time of descent $\left(t_{2}\right)=$ time of ascent $\left(t_{1}\right)=\frac{u}{g}$
$\therefore$ Total time of flight $\quad T=t_{1}+t_{2}=\frac{2 u}{g}$
$\Rightarrow\,\,\,\,\,\,u=\frac{g\left(t_{1}+t_{2}\right)}{2}$
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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.