Obstacle $3$: The Pit Eventually, the bear comes to rest. Suddenly, the ground falls out

underneath the box, and the bear falls straight into a pit $20$ m deep! The bear tries to climb

out, but the walls are frictionless and completely vertical. The bear yells for help! His

friend, a walrus, hears the bear call for help and comes to save him. The walrus throws a

rope to the bear in the pit and intends to lift the bear out by holding on to the other end of

the rope and sliding down a slope next to the pit at an angle of $40^($@$)$ from the vertical. The

slope has a coefficient of static friction of mu$\_($s$)=0\mathrm{.}4$ and kinetic friction of mu$\_($k$)=0\mathrm{.}2.$ Mass of bear is $25$kg$.$

a$.(15$ points$)$ What must be the walrus's minimum mass to pull the bear out of the pit?

b$.(12$ points$)$ If the walrus is $5$ kg greater than what you found in the previous part,

how fast is the walrus sliding down the slope when the bear reaches the top of the

pit?

c$.(7$ points$)$ How would the tension of the rope change if the polar bear had the mass

in part a vs the mass in part b$.$ Would the tension in the rope in part a be greater

than, less than, or equal to that in part b$?$ Explain your reasoning