If a freely falling body travels in the last second a distance equal to the distance travelled by it in the first three second, the time of the travel is:

Question

If a freely falling body travels in the last second a distance equal to the distance travelled by it in the first three second, the time of the travel is: (A) 6 sec (B) 5 sec (C) 4 sec (D) 3 sec

Tardigrade Admin · Accepted Answer

The distance covered in 3 sec, s3=u t+(1/2) g t2 or s3=0 × t+(1/2) 9.8 × 32 or s3=44.1 m The distance covered in last second s1 =u+(1/2) g(2 t-1) 44.1 =θ+(1/2) × 9.8(2 t-1) =4.9(2 t-1) As both the distances are equal then 4.9(2 t-1) =44.1 or 2 t-1 =(44.1/4.9)=9 or 2 t =9+1 ⋅=10 or t =5 sec

Q. If a freely falling body travels in the last second a distance equal to the distance travelled by it in the first three second, the time of the travel is:

6 sec

5 sec

4 sec

3 sec

The distance covered in 3sec, s3​=ut+21​gt2 or s3​=0×t+21​9.8×32 or s3​=44.1m The distance covered in last second s1​=u+21​g(2t−1) 44.1=θ+21​×9.8(2t−1) =4.9(2t−1) As both the distances are equal then 4.9(2t−1)=44.1 or 2t−1=4.944.1​=9 or 2t=9+1⋅=10 or t=5sec