Answer:
The force is 1.34 newtons and its direction is upward.
Explanation:
Choosing positive direction pointing towards the floor in this collision we're going to use the momentum-impulse theorem that states:
(1)
with the change in the momentum and J the impulse, with pi the initial momentum that is the momentum just before the collision and pf the final momentum th is the momentum just after the collision. The impulse J is also defined as:
(2)
with the average force and
the time the collision lasts
We can equate expressions (2) and (1):
Using the definition of linear momentum as mass (m) time velocity (v):
We can solve for Favg:
(3)
Now we should find the velocities vf and vi, we should do this using conservation of energy:
For the velocity the ball has just before reaches the floor:
With Ui the initial potential energy (there is not initial kinetic energy) and Kf the final kinetic energy (there is not final potential energy), then:
solving for vi:
For the velocity the ball has just after bounces the floor:
There is not initial potential energy because it's a floor level at this instant, and the there is not final kinetic energy because the ball has instantly zero velocity at its maximum height (hm), then:
solvig for vf:
Using vf and vi on (3):
The negative sign indicates the direction of the force is pointing away the floor