If a body travels half its total path in the last 1.50 s of its fall from rest, find the total time of its fall (in seconds).

time to fall is 3.914 seconds

Explanation:

given data

half distance time = 1.50 s

to find out

find the total time of its fall

solution

we consider here s is total distance

so equation of motion for distance

s = ut + 0.5 * at² ... 1

here s is distance and u is initial speed that is 0 and a is acceleration due to gravity = 9.8 and t is time

so for last 1.5 sec distance is 0.5 of its distance so equation will be

0.5 s = 0 + 0.5 * (9.8) * (t - 1.5) ² ... 1

and

velocity will be

v = u + at

so velocity v = 0 + 9.8 (t-1.5) ... 2

so first we find time

0.5 * (9.8) * (t - 1.5) ² = 9.8 (t-1.5) + 0.5 (9.8)

solve and we get t

t = 3.37 s

so time to fall is 3.914 seconds