A giant snowball of mass 4000 kg and radius 1 m is initially at rest at the top

Question

A giant snowball of mass 4000 kg and radius 1 m is
initially at rest at the top of a narrow ski slope (which we can
consider to be frictionless). The height difference h from the
top of the slope to the bottom is 50 m. Prof. D is
standing right in front of the snowball (initially at rest). The
snow ball is released from the top of the slope by Prof.
D’s arch-nemesis (Colonel Chemistry) and rolls down
the slope. As the snowball is spherical it has moment of
inertia I=2/5*m*r^2. Trying to escape being crushed by the
giant snowball, Prof. D starts skiing down the slope in a
straight line at the same time as the ball is released. Which
one of the following statements is correct?

A. The snowball will catch up with Prof. D and
squash him flat.
B. The distance between the snowball and Prof. D remains constant, he can only
escape when the slope widens and he can move to the side.
C. The snowball initially accelerates at the same rate as Prof. D, but eventually slows
down because of the rotational kinetic energy cost, and Prof. D will escape as he
does not have any rotational kinetic energy.
D. The distance between Prof. D and the snowball increases as they both move down
the slope and he easily escapes.


I'm stuck between C and D so if someone could show me how to figure this out that would be great!

Explanation / Answer

for the ball, we can see that the torque of gravity force. T=mg*R*sin0. so that a/R = T/I_0=mgRsin0/(7mR^2/5)=5sing0g/7R so a=5gsin0/7 the acceleration of prof is g*sin0. so that acceleration of prof is larger, so its D.

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