A 2.0 kg monkey slides down a 30 degree frictionless incline wiht an initial spe

Question

A 2.0 kg monkey slides down a 30 degree frictionless incline wiht an initial speed of 5.0 m/s. The monkey slides 20 m before reaching a spring with a spring constant 22 N/m. How fast is the monkey sliding just before reaching the spring and what is the maximum compression of the spring from equilibrium.

*The answer is 15 m/s, 5 m but I don't know how to arrive at that answer. In order to receive credit for this problem by professor stated that that we must begin the math with the equation U initial + K initial +W nc =U + K

Explanation / Answer

For the first part, use conservation of energy. Ui + ki= Uf + Ki Uf =0 Ignore the potential energy of the spring. h= 20 sin30 g= 9.8 vi = 5 m/s m= 2 kg You should get 15 m/s. For the last part, Kf= Uf 1/2mvf^2 = 1/2 kx^2 You should get around 5.

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