In a spring gun system, a spring with a spring force constant420 N/mN/m  , is compressed 0.13 mm . When fired, 80.9 %%of the elastic potential energy stored in the spring is eventuallyconverted into kinetic energy of a 6.10×10−2 kgkguniform ball that is rolling without slipping at the base of aramp. The ball continues to roll without slipping up the ramp with89.6 %% of the kinetic energy at the bottom converted into anincrease in gravitational potential energy at the instant itstops.
a)What is the velocity of the ball's center of mass at the baseof the ramp?
Express your answer using two significant figures.
b)At this position, what is the velocity of a point at the topof the ball?
Express your answer using two significant figures.
c)At this position, what is the speed of a point at the bottomof the ball?
Express your answer using two significant figures.
d)What maximum vertical height up the ramp does the ballmove?
Take the free fall acceleration to be 9.80m/s29.80m/s2. Expressyour answer using two significant figures.
