How Long Does It Take for a Person to Travel Up a Ramp Propelled by a Spring?

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Homework Statement

A 65 kg person sits in a chair that is attached to a spring of force constant 15,000 n/m. This spring is compressed 3 m and can project the person up to a 20 m high ramp. The person then slides up the 20º ramp, which has a coefficient of friction of 0.5, until the person stops at the top. How much time does it take the person to get up the ramp?

The answer given is 5.06 seconds.

Homework Equations

U_{g, 1} + U_{el, 1} + W_f + KE₁ = U_{g, 2} + U_{el, 2} + KE₂

The Attempt at a Solution

Two things confuse me. First of all, The distance it travels over the incline would be 20/cos(20) or 58.47m. This means that the amount of energy at the end has to equal

.5kX^2 - m*g*cos(20)*u_k*(d-X), or 61456 J.

The spring constant is so high that it isn't going to be at rest when it gets to the top. But even assuming that there's something at the top that it smashes into, so that it can have kinetic energy, I don't understand the relation to get a time.

I got this problem from this page: http://www.quia.com/pages/nhhonphys9.html and don't have a picture of the diagram, but I assume it's just a ramp with a 20-degree incline and height of 20m, with spring at the bottom.

 

[Doc Al]

To solve for the time, use kinematics, not energy methods. Find the person's acceleration.