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.
