Problem: A sled starts from rest at the top of the frictionless, hemispherical, snow-covered hill shown in the figure. Find an expression for the sleds speed when it is at angle exttip{phi }{phi}.Use Newtons laws to find the maximum speed the sled can have at angle exttip{phi }{phi} without leaving the surface.At what angle exttip{phi _{ m max}}{phi_max} does the sled "fly off" the hill?

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A sled starts from rest at the top of the frictionless, hemispherical, snow-covered hill shown in the figure. A figure shows a sled atop a hemispherical hill with radius R. As the sled slides down the hill, an angle phi between the radial line pointing towards its current position and the vertical line pointing at the top of the hill is formed.

Find an expression for the sleds speed when it is at angle .

Use Newtons laws to find the maximum speed the sled can have at angle without leaving the surface.

At what angle does the sled "fly off" the hill?