4. [20 pts] Two competitors, Alice and Bob, decide to race. There is a circular pool of water 20 meters in diameter. Looking from above, with the center being the origin (0, 0), they both start at the north end (0, 10) with the finish line being at the south end (0, -10). Alice decides to swim straight across the pool while Bob decides to run along the circumference of the pool. Alice swims at a constant speed of one meter per second. Bob runs at a constant speed of 7/2 meters per second. They begin the race at time t = 0, both starting at (0, 10). Alice's position at time t is (TA, YA) = (0, 10 -t). Bob's position at time t is (XB, yB) = (10 sin 20 , 10 cos 20 (a) [2 pts] At what time does Alice finish the race? (b) [2 pts] At what time does Bob finish the race? (c) [2 pts] Who won the race? (d) [6 pts] Find the distance d between Alice and Bob as a function of time t. (e) [8 pts] Find the rate of change of this distance d as a function of time t. Hint: It might be easier to deal with the square of the distance s(t) = d2(t). start A d(t] finish