Question:
A body is released from the top of the tower H metre high. It takes t second to reach the ground. Where is the body after t/2 second of release ?
A body is released from the top of the tower H metre high. It takes t second to reach the ground. Where is the body after t/2 second of release ?
Updated On: Jul 5, 2022
- at 3H/4 metre from the ground
- at H/2 metre from the ground
- at H/6 metre from the ground
- at H/4 metre from the ground
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The Correct Option is A
Solution and Explanation
Applying $S = ut + \frac{1}{2} gt^2 $ for the Ist case
$H = \frac{1}{2} gt^2$ .....(i)
Let $H_1$ be the height after t/2 secs. So distance of fall $= H - H_1$
$H - H_1 = \frac{1}{2} g \left( \frac{t}{2} \right)^2$
$\Rightarrow \, H - H_1 = \frac{1}{8} gt^2$ ....(ii)
Dividing (i) and (ii),
$\frac{H - H_1}{H} = \frac{1}{8} \times \frac{2}{1} = \frac{1}{4}$
$\Rightarrow \, 4H - 4H_1 = H \, \Rightarrow \, H_1 = \frac{3}{4} H $
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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.