Solving for Initial Velocity Up a Plane: A Homework Problem

[joseg707]

Homework Statement

A carton is given an initial speed of 3.0 m/s up a 22.0 degree plane. a.) How far up the plane will it go? b.) How much time elapses before it returns to its starting point? Ignore friction.

Homework Equations

F=ma

The Attempt at a Solution

I have no clue. If someone could point me in the right direction and try to explain what's going on I would very much appreciate it.

 

[joseg707]

I've been trying to figure it out. I know I'm supposed to break it into 2 equations, but I don't know how to express the 3.0 m/s velocity in the x equation.

\sumF_x=mg*sin\theta=ma_x

\sumF_y=F_N-mg*cos\theta=ma_y=0

Is that right? If it is I still don't know where to go from here

 

[jgens]

Use the equation vf^2 = vi^2 + 2(a_x)(s).

 

[joseg707]

But I don't know the time, nor the acceleration.

 

[jgens]

You have both the initial and final velocities so all you need right now is the acceleration in the x direction, which you can find by using mg = Fncos(theta) and a_x = gsin(theta).

 

[joseg707]

Oh, ok. Now I get it. You put an (s) in the equation which threw me off. I found the distance and the time it took to reach the max point, but how do I get the total time? Should I just double the time it took to get to the highest point?