III) A skier skis from rest from a vertical height over two successively lower hills of vertical height and (See Figure below). The summit of the third hill fits a circle of radius centered at height 0 m. Friction with the snow and air resistance are negligible. (a) Find the speeds of the skier at and . (b) Does the skier leave the surface at ? If not, how large should be so that the skier just leaves the surface at ? Justify your answer quantitatively.

a)

and

b) Skier does not leave the surface at .

We want at . Since , we must have

IV) A 20-g bullet is fired in the x-direction into a block of wood of mass 15 kg at rest (See Figure below). The speed of the bullet before entry is . (a) What is the speed of the block just after the bullet has become embedded? (b) What distance d will the block slide on a surface with coefficient of friction equal to 0.50 before coming to rest?

a)

b)