To solve this problem, we must assume that the man undergoes constant acceleration as he goes down the river (therefore no other forces must act on him except gravity). Therefore we can use the formula below to calculate for the duration of his fall:
y = y0 + v0 t + 0.5 a t^2
where y is the distance and y0 = 0 since we set the reference point at the bridge, v0 is the initial velocity and is also equal to v0 = 0 since the man started from rest, therefore the equation becomes:
y = 0 + 0 t + 0.5 a t^2
y = 0.5 a t^2
Rewriting in terms of t:
t^2 = 2 y / a
t = sqrt (2y / a)
a is acceleration due to gravity = 9.8 m/s^2
t = sqrt [2 * 23 / 9.8]
t = 2.17 s
Therefore the jump last only about 2.17 seconds.
