A body is dropped from rest from a height H above the ground. The distance travelled by it during the last one second of its fall is three-fourths of the total height H. Neglect air resistance. The total time of fall is:
Options

Question

A body is dropped from rest from a height H above the ground. The distance travelled by it during the last one second of its fall is three-fourths of the total height H. Neglect air resistance. The total time of fall is:

Options

G1 Physics · Accepted Answer

If total time of fall is T, then H = (1/2)gT^2. Distance in the last second = (1/2)g[T^2 - (T - 1)^2] = (1/2)g(2T - 1). Given this equals 3H/4: (2T - 1)/T^2 = 3/4. Thus 3T^2 - 8T + 4 = 0, giving T = 2 s or 2/3 s. Since a 'last one second' interval requires T > 1 s, T = 2 s. Hence option B is correct.