Calculas Derivitive Problem... :? Uh Oh :/?

dave

A balloon is rising vertically above a level straight road at a constant rate of 2.5 ft/sec. Just when the ballon is 80 ft above the ground a bicycle moving at a constant rate of 25 ft/sec passes directly under it. How fast is the distance between the bicycle and the ballon increasing 4 seconds later?

basildreams

dx/dt = 2.5 ft/sec

dy/dt = 25 ft/sec

80/2.5 = 32 seconds have passed

32 + 4 = 36 seconds

36 x 2.5 = 90

so, x = 90

36 x 25 = 900

so, y = 800

s = (x² + y²)^ 1/2

ds/dt = ((x² + y²)^ (-1/2))(x(dx/dt) + y(dy/dt))

ds/dt = ((90² + 900²)^ (/1/2)) ((90 x 2.5) + (900 x 25)

ds/dt is approximately 25.125 ft/sec