An engineer wishes to design a roller coaster so that the cars will not fall when they are at the top of their
circular path.
A 500 kg roller coaster car is designed to travel at 20
m/s at the top of the circle. The engineer wants to
make the circle as large as possible while still being
at least one quarter the maximum radius for safety
reasons. How large can the radius of the circle be?

Two students, each riding bicycles, start from the same apartment building and ride to the same building on campus, but each takes a different route. the first student rides 1100 m due east and then turns due north and travels another 1430 m before arriving at the destination. the second student heads due north for 1930 m and then turns and heads directly toward the destination. at the turning point, how far is the second student from the destination?