9.8 Of course, you know the liquid density owing to the fact that you know the mass and volume when the can is filled. This is enough to calculate the liquid mass when the can is filled to a depth x. It is advisable to plot the resulting center of mass versus x.
9.15 You can easily find the velocity of the projectile at the top of the trajectory. At that point, apply conservation of momentum. If the falling particle has no initial velocity ...
9.45 Don't overthink this one. Conservation of momentum before and after along x and y axes. Symmetry is useful.
9.48 Both energy and momentum must be conserved, right?
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