MathDB

A ball of mass

M

and radius

R

has a moment of inertia of

I=\frac{2}{5}MR^2

. The ball is released from rest and rolls down the ramp with no frictional loss of energy. The ball is projected vertically upward off a ramp as shown in the diagram, reaching a maximum height

y_{max}

above the point where it leaves the ramp. Determine the maximum height of the projectile

y_{max}

in terms of

h

. [asy] size(250); import roundedpath; path A=(0,0)--(5,-12)--(20,-12)--(20,-10); draw(roundedpath(A,1),linewidth(1.5)); draw((25,-10)--(12,-10),dashed+linewidth(0.5)); filldraw(circle((1.7,-1),1),lightgray); draw((25,-1)--(-1.5,-1),dashed+linewidth(0.5)); draw((23,-9.5)--(23,-1.5),Arrows(size=5)); label(scale(1.1)*"

h

",(23,-6.5),2*E); [/asy] (A)

h

(B)

\frac{25}{49}h

(C)

\frac{2}{5}h

(D)

\frac{5}{7}h

(E)

\frac{7}{5}h

13

Problems(1)