Conservation of Energy Problem.

[TwinGemini14]

A cart, initially at rest, slides down a frictionless ramp onto a horizontal frictionless surface which is a distance h below the original position of the cart. It then collides with the free end of a relaxed horizontal spring, the other end of which is fixed to a wall. As a result the spring compresses a distance D.

Suppose now the initial height is changed to 2h. How far will the spring now compress?

A) sqrt(2)D
B) 2D
C) 4D

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Initially: mgh = 0.5 k D^2

Suppose: mg(2h) = 0.5 k (2D)^2

So... the spring will now compress 4D. Is this correct?

 

[LowlyPion]

Maybe rework your math again?

And remember D is unknown.