Obstacle $2$: Hooligans The path on the other side of the Lava Pit is completely frictionless,

and the bear slides on the path with the x component of his velocity found in question $1$ b $.$

Further up the path is a group of $3$ hooligans straight in front of the bear. For fun, each

hooligan takes a rock of mass $3$ kg $,$ pulls it back $0\mathrm{.}5$ m in a slingshot with an approximate

spring constant of $200$N$//$m and releases the rock directly at the bear. The bear manages to

catch all three rocks. The mass of the bear is $25$kg$.$

a$.(12$ points$)$ How fast is the bear moving after he catches all the rocks?

b$.(12$ points$)$ The path in front of the bear makes an abrupt right$-$hand turn. The bear

needs to make the turn and continue moving down the path. Describe a way for the

bear to make the turn and approximate the speed the bear is going after he makes it$.$

Be as specific as possible. You may have to make some approximations and

assumptions to answer this question. State each approximation and assumption you

are making and why you made it$.$