Forces and Motion - Ramp Question

[Scimitar]

Homework Statement

There is a ramp, with an angle of 30 degrees. The height of the ramp is 10 m. There is a mass at the bottom of the ramp. Assuming the ramp is frictionless, determine the initial speed that the mass must have so that it just comes to rest at the top of the ramp.

Part 2 is to repeat with a coefficient of static friction of 0.200.

Homework Equations

I assume all kinematics equations and the use of Newton's law equations.

The Attempt at a Solution

I tried finding the x and y components of velocity by using the height (10m) as distance, v2 = 0m/s and acceleration as 9.8 m/s^2. However, I was not sure how that would work for the horizontal component. I attempted to find the acceleration using Newtons second law; ma = F - mgsin30, however that leaves me with two variables. I was able to get the answer for the first part by using the kinematics equation 2da = v2^2 - v1^2 and using d = 10m, v2 = 0m/s, a = -9.8m/s^2 however I do not know how that works.

The answer for part 1 is 14 m/s, the answer for part 2 is 16.2 m/s.

 

[nasu]

You can use energy conservation. It's the easiest way.
I don't really understand your attempt.

 

[Maiq]

^ It looks like its just mgh=(1/2)mΔv^{2}