Question

Related rates fixed buoy? A boat passes a fixed buoy at 9

a.m. heading due west at 3 miles per hour. Another boat passes the same buoy at 10
a.m. heading due north at 5 miles per hour. How fast is the distance between the boats changing at 11:30
a.m.? I can't figure this out! I would appreciate all the help I can get! Thank you!

Answer 1

Hello there.

Related rates fixed buoy? A boat passes a fixed buoy at 9
a.m. heading due west at 3 miles per hour. Another boat passes the same buoy at 10
a.m. heading due north at 5 miles per hour. How fast is the distance between the boats changing at 11:30
a.m.?

5.6569 mph

Answer 2

For the answer to the question above, let coordinates of boat B at 10 am at the buoy be (0,0)
then co-ordinates of boat A is (3,0)

let dist. between A & B be z, then at time t hrs after 10
z² = (3+3t)² +(5t)² = 34t² +18t +9,
value 112.5 at t = 1.5

2z.dz/dt = 2*34t +2*9
dz/dt = (34t +9)/z
= (34*1.5 + 9)/√112.5
= 5.6569 mph