First of all, it might rise all the way to the top and back down the other side! We don't know that yet. Let's assume that it doesn't get all the way to the top and solve for what height we get. If this is greater than 1m, then we know that it get's to the other side.
So what is the physics at the point where the block reaches it's maximum height. Well in the reference frame of the hump, the block rises up it and comes to a maximum as pictured above. At this point the block is stationary relative to the hump. That means that at this point, the block and the hump have the same velocity. We already considered this type of problem earlier! It's identical to the problem of inelastic collisions. The velocity in this case is just the center of mass velocity of the system which by eqn. 1.37 is
This is the answer to part b of the problem.
At that point the total kinetic energy of the system is
The inital kinetic energy was just 
, so the difference in these
two kinetic energies must be the potential energy mgh (by conservation of
energy).
Therefore
or
This is less than a meter so the block doesn't go over the top. This is the answer to part a of the problem.
Now how do we figure out c? We know that momentum is conserved and energy is conserved, so we this is an example of an elastic collision. Even though it is a little bizarre, it is a collision nevertheless.
So we can use our painfully derived formulae 1.62 and
1.63 to calculate the final velocities of the
objects. In this case 
, 
and 
.
Pluggin these in, we see that 
, and 
.
So the block stops completely and the hump moves off with a
velocity of 1m/s.
Notice how fiendishly difficult this problem would have been to solve using F=ma!
We could have solved this whole problem starting from Newton's three laws of motion. It would have been much much harder. Although conservation of momentum and energy are a consequence of Newton's laws, for many questions, they provide much insight to what's going on. You shouldn't forget however that they are a consequence of Newton's laws. They contain no extra information.