Question

A body dropped from top of a tower, covers a distance 7 h in last second of its motion, where h is distance covered in first second. The total time of flight (in seconds) will be

Answer 1

In the first second of the journey, the body travels:

h(1)=g/2 (1)²

=4.9m

In the last second of the journey, the body falls 4.9 x 7, or 34.3 meters. Let t be the total falling time, and t-1 be time fallen before the last second. Then:

h(t)-h(t-1)=34.3

g/2 t² - (g/2 (t-1)²)=34.3

4.9t² - (4.9(t²-2t+1)=34.3

9.8t-4.9=34.3

9.8t=39.2

t=4 seconds total time fallen