Question

A body falls freely from rest. It covers as much distance in the last second of its motion as covered in the first three seconds. The body has fallen for a time of
A. 3s
B. 5s
C. 7s
D. 9s

Answer 1

Hint: Use a kinematic equation to solve this problem. You can use the free fall body concept. Free falling body is the only body under the influence of gravity. Do not consider resistance of air present in the atmosphere.

Complete Step-by-Step solution:
In the given question, we can see that no other force is acting on the body other than gravitational force, not even resistance of air is affecting the body. That means we can consider it as a free fall body.
Given that, in three seconds, a body covers the distance as much as in the last three second.
By writing kinematic the equation,
Distance covered by body in three seconds,
${{D}_{1}}=\dfrac{g\times{{3}^{2}}}{2}$
Distance covered by body in last second,
${{D}_{2}}=\dfrac{g\times{{t}^{2}}}{2}$
Distance covered by the body one before influence,
${{D}_{3}}=\dfrac{g\times{{(t-1)}^{2}}}{2}$
According to given question
${{D}_{1}}={{D}_{3}}-{{D}_{2}}$
Cancel common factor, we get
$\begin{align}
  & {{3}^{2}}={{t}^{2}}-{{(t-1)}^{2}} \\
 & 9={{t}^{2}}-({{t}^{2}}-2t+1) \\
\end{align}$
Remove parenthesis,
$\begin{align}
  & 9={{t}^{2}}-{{t}^{2}}+2t-1 \\
 &\text{ we get} \\
 & 9=2t-1 \\
 & 2t=10 \\
 & \text{we have} \\
 & t=5s \\
\end{align}$
The body has fallen for a time of 5 second.

Notes: Free fall body concept is an important concept. Students can explore more on free fall bodies by relating it with different laws like Newton's law of motion. Students should not be confused between weightlessness and free fall.