More optimization problem practice with Scuba Steve.

1. Can Scuba Steve Escape the
Underground Cavern?!?
AKA more
Optimization
practice
Comino Caves II by flickr user Michael Aston

2. Scuba Steve is on a pleasure dive in a large underwater cavern when his trusty companion
Scuba Bev-Dog, a known mysophobic, spots a major leak in his tank. With a glance at Steve's
PSI reading and some quick mental math, Scuba Bev-Dog calculates that Steve has only 90
seconds to reach the exit of the cave and the safety of air (a small hole 75 above him and 200
feet due East.) Since Scuba Steve can only swim 2 ft/sec, he realizes that he could never
make it to the exit in time. Luckily Bev-Dog remembers that 30 ft above them lies a strong
underwater current (with a negligible height) pushing exactly due East at 2 ft/sec. Realizing he
could utilize this current to minimize his time and possibly save his life he immediately sets off
towards the current 30 feet above him an an angle of 45 degrees from the bottom of the
cavern. On the trip towards the current, Steve rapidly does some calculus to determine how
long he should swim in the current to minimize his time. He finds his solution upon entering
the current and sets off to beat the clock.
1. Give Scuba Steve's time of ascent function.
2. For what distance should Scuba Steve swim
in the current in order to minimize his time?
3. Does Scuba Steve survive?
4. If so, by how many seconds did he succeed?
5. If not, by how many seconds did he fall short
of survival?