D^2 = x^2 + y^2
2 D dD/dt = 2 x dx/dt + 2 y dy/dt
or
dD/dt = (x dx/dt + y dy/dt)/D
at t = 0
x = 0
y = 150
at t = 10
x = 580
y = 150+100 = 250
D = sqrt(580^2+250^2) = 631.6
dx/dt = 58
dy/dt = 10
so plug into
dD/dt = (x dx/dt + y dy/dt)/D
A hot air balloon is 150 ft above the ground when a motorcycle passes beneath it (traveling in a striaght line on a horizontal road) going 58 ft/sec. If the balloon is rising vertically at a rate of 10 ft/sec, what is the rate of change of the distance between the motorcycle and the balloon 10 seconds later?
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