Magnitude of the Force of a kick to a basketball

[smedearis]

Homework Statement

A 0.5 kg basketball is rolling by you at 3.9 m/s. As it goes by, you give it a quick kick perpendicular to its path. Your foot is in contact with the ball for 0.002 s. The ball eventually rolls at an angle of theta = 24 degrees from its original direction.

Homework Equations

DeltaP=Fnet*DeltaT
Pinitial=.5*0.5*3.9^2

The Attempt at a Solution

I know what Pinitial is, but what is Pfinal? Where does the theta come in, force or final velocity?

 

[radou]

DeltaP=Fnet*DeltaT
Pinitial=.5*0.5*3.9^2

The impulse equals change in momentum, not kinetic energy, you may want to consider this, first.

 

[smedearis]

ok, impulse =Fnet*DeltaT=DeltaP(change in momentum), right?

am i still assuming that p=mv, so m*Vfinal-m*Vinitial=DeltaP
where would i find the Vfinal?

 

[radou]

ok, impulse =Fnet*DeltaT=DeltaP(change in momentum), right?

am i still assuming that p=mv, so m*Vfinal-m*Vinitial=DeltaP
where would i find the Vfinal?

It is practical to work with vectors. Assume that the initial direction of the velocity of the ball is $$\vec{i}$$, and the direction of the force (i.e. impulse) $$\vec{j}$$. Further on, use $$\vec{v}_{2} = v_{2}\cos(30)\vec{i}+v_{2}\sin(30)\vec{j}$$. Form a vector equation based on $$\vec{I} = m\vec{v}_{2}-m\vec{v}_{1}$$, where $$\vec{v}_{2}$$ is the final, and $$\vec{v}_{1}$$ the initial velocity. After 'solving for' $$\vec{i}$$ and for $$\vec{j}$$, you can calculate both the final velocity and the force.

 

[smedearis]

I don't think I'm following you on this. how and why are you using cos(30) and sin(30)?

 

[radou]

I don't think I'm following you on this. how and why are you using cos(30) and sin(30)?

I'm sorry, I meant 24 degrees, my mistake. Do you follow now?

 

[smedearis]

I'm still not understanding.
To find Vf, I use Vi*sin(24)+Vi*sin(24), b/c previously, you said that i need to multiply the trigs by the Vf, but i don't know what that is.

how do i know the direction of the force and velocity?

 

[radou]

I'm still not understanding.
To find Vf, I use Vi*sin(24)+Vi*sin(24), b/c previously, you said that i need to multiply the trigs by the Vf, but i don't know what that is.

how do i know the direction of the force and velocity?

Ok, I'll assume you're familiar with basic vector algebra. First of all, do you agree with the equation I wrote: $$\vec{I} = m\vec{v}_{2}-m\vec{v}_{1}$$? (*)

Further on, you know that the impulse equals $$\vec{I}=\vec{F}\cdot t$$. Let the magnitude of the force (which is unknown, but that doesn't matter) be F. So now you have $$\vec{I}=F \vec{j} \cdot t$$. The direction perpendicular to $$\vec{j}$$ is $$\vec{i}$$, so the initial momentum equals $$m \vec{v}_{1} = m 3.9 \vec{i}$$. Now we have the condition satisfied that the force acted (i.e. the impulse) in a direction perpendicular to the initial direction of the ball's motion, right? Now, all we have to do is plug these values back into the equation (*), along with $$\vec{v}_{2} = v_{2}\cos(24)\vec{i}+v_{2}\sin(24)\vec{j}$$.

You may want to draw a simple sketch, It should help, too.