Question

So lost... could someone please help me with setting up this problem?

A football (m = 0.4 kg) is kicked from rest to a final velocity of vf = 36 m/s @50⁰. During the kick, the ball compresses about 10 cm while the kicker’s foot is in contact with it. Assuming the force exerted on the football by the kicker is constant and much larger than other interactions, (hint: consider the average velocity)
a) How much time is the kicker in contact with the ball?
b) What is the magnitude of the force the kicker exerts on the football?

Answer 1

I know the formula for average velocity is ½(vi + vf) but that only gets me to (1/2)( 36 m/s @50⁰). I have a similar problem the teacher worked during class, but am having trouble following that.

Answer 2

I drew a picture showing my coordinates and system vs. surroundings.

Answer 3

With the football, can we say that the force acts through a distance of 10cm and so does work equal to F*0.1 J
This should equal the kinetic energy given to the ball, which we can calculate from the information given and from there we can find F.
Then we can say that F*t will equal the momentum given to the ball, which we also know, so you can then find t.
The question also tells you that you can ignore gravity here because the force of the kick is so much larger.