Question

A man walks across a bridge at the rate of 5 ft/s as a boat passes directly beneath him at 10 ft/s. If the bridge is 10 ft above the boat, how fast are the man and the boat separating 1 second later?

Answer 1

at 1 second d = sqrt(10^2 + 10^2 + 5^2)
= sqrt 225

d^2 = 100 + 25 t^2 + 100 t^2
d^2 = 100 + 250 t^2

2 d dd/dt = 500 t
v = dd/dt = 250 t/d

at t = 1
v = 250/15 = 16.7 ft/s