(Solved): 3) A dart of mass m=0.1kg is compressed against a spring to half of its unstretched length on a h ...

3) A dart of mass $m=0.1\mathrm{kg}$ is compressed against a spring to half of its unstretched length on a horizontal surface. It is released at rest from the compressed spring then hit a wood block of 0.2 $\mathrm{kg}$ mass that is at rest. The dart gets into the block and they move together along an inclined surface of angle $\theta$. Assume all surface are frictionless. Find the maximum height the block and dart together can go up on the inclined surface. Assume the unstretched length of the spring is $L=12.0\mathrm{cm}$ and the spring constant is $k=1000.0\frac{\mathrm{N}}{\mathrm{m}}$.