Question

A body is falling freely. If the displacement in the last second is equal to the displacement in the first 3 seconds, find the time of free fall.
1. 5 s
2. 10 s
3. 15 s
4. 20 s

Answer 1

Hi friend
here is your answer

s = ut + (1/2)at2
for the first three second
as 
u = 0 m/s, t = 3 ,a = g = 10 m/s2
So,
s = 0 + (1/2)x10x32
thus,
s = 45m  ____________1

and

let the total time taken to reach ground be 'n' seconds.
The displacement in the last second of motion or the nth second is given by this standard relation

sn =  u +(1/2).a.(2n - 1)
sn = 0 + (1/2) x 10.x (2n - 1)
sn = 5(2n - 1)  ...........................(2)

now, we are given

s = sn(displacement in the last second is equal to the displacement in the first 3 seconds)

45 = 5(2n - 1)
2n -1 = 9
thus,
n = 5s
so, total time taken will be 5s + 1s = 6s

by the way your question is wrong you have not given the option of 6s
please correct your question

Hope this will help you
please mark as brainliest

Answer 2

Answer:

1. 5 s

Explanation:

Distance travelled in first 3 seconds = (1/2)gt2 = (1/2)×9.8×9 = 44.1 m

 

Let t be the time taken to travel the total height;

 

velocity at (t-1)th second = g×(t-1);

distance travelled at the last second = g(t-1)-(1/2)g = g×(t-1.5) = 44.1;

hence t = (44.1/9.8)+0.5 = 5 s