Problem 7.12

7.12. a)

Since , the system will move from the position shown in figure P7.11. The initial energy of the system is equal to the final energy of the system since there are no non-conservative forces. Also, the final velocities of the two masses will be the same as they are tied together. Looking at the final time as the time when hits the ground we find that

Solving for v yields

b)

Since the mass has a non zero kinetic energy when hits the ground, it will rise an additional height determined again from conservation of energy.

solving for and plugging in the value for v found in part a, we find

so the total height that reaches is given by , or