Kinematics playgound slide problem

[professor97]

Homework Statement

You place a m=2kg block at the bottom of a playground slide and give it a quick kick, giving it an initial speed of vi=12m/s. The slide is inclined at an angle of 35 degrees and the coefficient of kinetic friction between the block and the slide is mu_k=0.2. Use g=9.8m/s/s.
a) What is the magnitude of the friction force on the block while it is moving on the slide? **I found this to (correctly) be 3.2 N
b) Assume the slide is sufficiently long that the block does not go over the top. How far up the slide does the block go?
c) If the block slides back down, what will its speed be at the bottom?

I've been trying to solve this using kinematics equations involving constant acceleration. I know for part (b) that the final velocity is 0 m/s at the top of the ramp. I'm not sure however if the vi needs to be resolved into components, like I had to do to find the frictional force. Also, it was hinted that I might want to avoid finding time, so I've been dealing with the equation vf^2=vi^2+2ad Can the acceleration be found from net force? Would Fnet,x just be 3.2 N? I feel like this problem is a lot simpler than I'm making it out to be. Thanks for any and all help.

 

[gneill]

If you've been given a hint to avoid finding time (and hence using equations involving time), then you should be thinking "conservation of energy". Remember that friction forces "burn" energy over the distance traveled.

But you could still use basic kinematics. Besides friction, what other force is acting on the block along the direction of the slope? Hint: It's the one perpendicular to the normal force that you used to find the friction force.