Please explain in detail how to solvethis problem because this is for my finals

Question

Please explain in detail how to solvethis problem because this is for my finals review. Thankyou!!!! 8) The 2.0 kg box shown below is slidingwith an initial velocity of 3.0 m/s before it slides down theincline and then collides with a massless spring of spring constant4.0 N/m. By how much is the spring compressed if the box started ath = 2.0 m?
A) 6.0 m B) 4.9 m C) 5.5 m D) 3.2 m E) 4.0 m Please explain in detail how to solvethis problem because this is for my finals review. Thankyou!!!! 8) The 2.0 kg box shown below is slidingwith an initial velocity of 3.0 m/s before it slides down theincline and then collides with a massless spring of spring constant4.0 N/m. By how much is the spring compressed if the box started ath = 2.0 m?
A) 6.0 m B) 4.9 m C) 5.5 m D) 3.2 m E) 4.0 m

Explanation / Answer

At initial condition , velocity = 3.0 m/s So kinetic energy = mv2/2 = 2*9/2=9 J Gravitational potential energy =mgh = 2.0*9.8*2=39.2 J Total energy = 48.2 J Finally when spring is completely compressed , whole energy is in form of plastic potential energy , So kx2/2 = 48.2 x = 4.9 m

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