Answer:
Approximately
.
(Assuming that
and that air resistance is negligible.)
Step-by-step explanation:
Under the assumptions, the acceleration of the child would be constantly
while the child was in the air.
Apply the SUVAT equation
to find the velocity
of the child right before landing:
, where:
is the initial velocity of the child,
is the vertical acceleration, and
is the vertical displacement (change in height.)
The child is at rest
after contact. During that
, velocity would have changed by
. Momentum of the child would have changed by
, where
is the mass of the child.
Divide this change in momentum by the duration
to find the average net force:
.
There are two forces on the child: upward normal force from the ground
and downward gravitational attraction
from the Earth. The resultant force on the child points upwards:
.
Rearrange this equation to find the normal force on the child:
.
This normal force from the ground on the child is the reaction to the force that the child exerted on the ground. The two forces will have the same magnitude: approximately
. Hence, the child would have exerted an average force of approximately
on the ground during that
.