Question

A stone fell from the top of a tower to the ground in 8
seconds. How much time did it take to cover the first
quarter of the distance starting from the top?
[Odisha 2015-16)
(A)4 seconds (B) 5 seconds
(C) 6 seconds (D) 8 seconds​

Answer 1

Answer:

4 second

by using equation of motion

Answer 2

Answer:

The time taken to cover the first quarter of the distance starting from the top is 4 seconds i.e.option(A).

Explanation:

This is the formula-based question. We will use the equation of motion to solve this question.

First, we need to find the total height of the tower.

So,

$H=ut+\frac{1}{2}gt^2$               (1)

H=height of the tower

u=initial velocity

t=time

g=acceleration due to gravity=10ms⁻²

For the given situation initial velocity will be zero.    

and total time is =8sec

By substituting the given values in equation (1) we get;

$H=0\times 8+\frac{1}{2}10\times 8^2=320m$

Now as per the question,

The quarter distance will be given as,

$S=\frac{H}{4}$               (2)

Where,

S=quatrter distance

H=total height of the tower

So,

$S=\frac{320}{4}=80m$

Now we will use equation (1) to find the time taken to cover the first quarter distance,

$80=0\times t+\frac{1}{2}10\times t^2$

$t^2=\frac{80\times 2}{10}=16$

$t=\sqrt{16} =4s$

Hence, the time taken to cover the first quarter of the distance starting from the top is 4 seconds i.e.option(A).