Question: A body falling from a high Minaret travels \[40m\] in the last \[\;2\;\] seconds of its fall to the ...

Question

A body falling from a high Minaret travels $40m$ in the last $\;2\;$ seconds of its fall to the ground. The height of Minaret in meters is
( take $g = 10m/{s^2}$ )
A. $60$
B. $45$
C. $80$
D. $50$

Answer 1

Solution

The key to answering this question is provided by the equation of motions. The physical behavior of the object includes position, velocity, acceleration, etc. These physical behaviors of an object can be explained using equations of motion. We need to divide the question into two parts: the last two seconds when the object falls in the ground and before two seconds. Substituting the equation of motion in both cases we can find the height of the minaret.

Complete answer:
The second equation of motion gives us the formula,
$s = ut + \dfrac{1}{2}a{t^2}$
Here $s$ is the displacement of the object
$u$ is the initial velocity.
$a$ is the acceleration of the body.
$t$ is the time taken.
When a body falls freely under the influence of gravity and when its initial velocity is zero and acceleration is only due to gravity and g remains constant when height $\;h$ is not a large quantity, the equation of motion will be reduced to the form,
Let $h$ be the total height and $t$ be the total time taken.
Therefore for the second case is when Minaret travels $40m$ that is $h - 40$ in the last $\;2\;$ seconds that is $t - 2$ of its fall to the ground. Substituting in the above equation,
$h - 40 = 5({t^2} + 4 - 4t)$ ………. (1)
For total height and the total time is taken we can write the above equation as,
………. (2)
$h = 5{t^2}$ …… (3)
Substituting (3) in (1)
$5{t^2} - 40 = 5\left( {{t^2} + 4 - 4t} \right)$
$\Rightarrow 5{t^2} - 40 = 5{t^2} + 20 - 20t$
$\Rightarrow 20t = 60$
$\Rightarrow t = 3s$ ……… (4)
Substituting (4) in (1)
$h = 5{(3)^2}$
$h = 45m$

Therefore the correct option is B.

Note:
Equations of motion are used to describe the physical system’s behavior using a set of mathematical functions. They are usually used to calculate the components of motion. It is used to calculate different parameters involved in a motion such as velocity, time, acceleration, etc.