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**1. Homework Statement**

A ball of mass M and radius R has a moment of inertia of I =2/5MR. The ball is released from rest and rolls

down the ramp with no frictional loss of energy. The ball is projected vertically upward o a ramp as shown in

the diagram, reaching a maximum height ymax above the point where it leaves the ramp. Determine the maximum

height of the projectile ymax in terms of h

The image is cut off but h is the height from the top of the ramp to the ball

**2. Homework Equations**

PE=1/2mv^2

Rotational KE= 1/2 I omega^2

KE= 1/2mv^2

**3. The Attempt at a Solution**

Using x as the distance between the bottom and top of the ramp:

mg(h+x) = 1/2mv^2+1/2I omega^2 =1/2mv^2 + 1/2(2/5mr^2)omega^2 = 1/2mv^2 + 1/5mv^2 = 7/10mv^2

7/10mv^2=mgx + 1/2mv'^2

1/2mv'^2 = ymax

im stuck here D: any hints?