Question:
A body falls freely from the top of a tower. It covers $36\%$ of the total height in the last second before striking the ground level. The height of the tower is
A body falls freely from the top of a tower. It covers $36\%$ of the total height in the last second before striking the ground level. The height of the tower is
Updated On: Jul 5, 2022
- 50m
- 75m
- 100m
- 125m
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The Correct Option is D
Solution and Explanation
Let height of tower is h and body takes time t to reach the ground when it falls freely.
$\therefore h=\frac{1}{2} g t^{2} \ldots$(i)
In last second ie, the sec body travels $=0.36 h$
It means in rest of the time ie, in $(t-1) \sec$
it travels $=h-0.36\, h=0.64\, h$
Now, applying equation of motion for $(t-1) \sec$
$0.64 \,h=\frac{1}{2} g(t-1)^{2} \ldots $ (ii)
From Eqs. (i) and (ii), we get
$t=5 \,s$ and $h=125\, m$
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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.