Question

1. A body falling from a height describes 19/100 of the total height in the last second. It is
falling for t sec. From a height h. Then t, h are.
1) 10 sec, 490 m
2) 10/19 sec. 490 m 3) Both
4) None​

Answer 1

Answer:

(1) 10 s ; 490 m

Explanation:

Let the total time taken be "T" seconds

Use equation of motion

• S = ut + 0.5at²

For total fall

h = (0 × T) + (0.5gT²)

h = 0.5gT² .......(1)

For the time t = T - 1 seconds

h - 19h/100 = (0 × T) + 0.5g(T - 1)²

81h/100 = 0.5g(T - 1)² .......(2)

Divide equations (1) and (2)

h / (81h/100) = 0.5gT² / [0.5g(T - 1)²]

100/81 = [T / (T - 1)]²

10/9 = T / (T - 1)

10T - 10 = 9T

T = 10 seconds

Substitute T = 10 s in equation (1)

h = 0.5gT²

= 0.5 × 9.8 m/s² × (10 s)²

= 490 m