Question

an object is dropped from the top of a tower the distance it covers in the last second is 7 times the distance it covered in a first second find the time of flight

Answer 1

distance covered by object in first second=x let distance covered by the object in second time= 7x

in the first second of journey , the body travelled
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