Question:
A body falling from a high minaret travels 40 m in the last 2 s of its fall to ground. Height of minaret is [Take $g = 10 \,m \,s^{-2}$]
A body falling from a high minaret travels 40 m in the last 2 s of its fall to ground. Height of minaret is [Take $g = 10 \,m \,s^{-2}$]
Updated On: Jul 5, 2022
- 60 m
- 45 m
- 80 m
- 50 m
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The Correct Option is B
Solution and Explanation
Let h be total height and t be the total time of flight. Then,
$h = \frac{1}{2}? 10 ? t^{2} = 5t^{2}\quad\cdots\left(i\right)$
and $h - 40 = \frac{1}{2} ? 10 ?\left( t - 2\right)^{2} = 5\left(t^{2} + 4 - 4t\right)$
Using $\left(i\right)$, we get
$5t^{2} - 40 = 5\left(t^{2} - 4 - 4t\right)$ or $5t^{2} - 40 = 5t^{2} + 20 - 20t$
or $20t = 60$ or $t = 3\, s$
$\therefore\quad h = 5\left(3\right)^{2} = 45 \,m$
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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.