Answer:
The tennis ball hit the ground at a speed of approximately
.
The tennis ball bounced away from the ground at a speed of approximately
.
The average acceleration of the tennis ball during the contact was approximately
.
Step-by-step explanation:
If an object of mass
is travelling at a speed of
, the kinetic energy
of that object will be
. At a height of
above the ground, the gravitational potential energy
of that object will be
.
If the drag on the tennis ball is negligible, energy will be conserved:
.
In particular, if the tennis ball was released from a height of
, its speed
right before landing will ensure that
. Rearrange to obtain
. Since the tennis ball was released from a height of
, the speed of the ball right before landing will be:
.
The same reasoning applies when the tennis ball bounces off the ground:
.
If the tennis ball bounced off the ground at a speed of
, the height
that this tennis ball will reach should also satisfy
. Rearrange to obtain
. Since the tennis ball reached a height of
, it would have bounced off the ground at a speed of:
.
Acceleration measures the rate of change in velocity. The velocity of this tennis ball was downward right before landing, at approximately
(the negative sign indicates the direction of velocity.) The velocity of this ball points upward after bouncing back, at approximately
.
Hence, the change in the velocity of this tennis ball will be:
.
Since this change in velocity required a duration of
, the average acceleration of this tennis ball would have been:
.