at noon A is 150 km west of a ship B .Ship A is sailling east at 35 km/h , and ship B is sailling north at 25 km/h. How fast is the distance between the ships changing at 4 pm ?

Answer 1

the distance between the ships at time t is

d^2 = (150-35t)^2 + (25t)^2
at t=4,
d^2 = (150-140)^2 + (100)^2 = 100 + 10000 = 10100, so d=100.5

2d dd/dt = 2(150-35t)(-35) + 2(25t)(25)
at t=4,

201 dd/dt = -700 + 5000
dd/dt = 21.39km/h