Question

Two drivers begin at the same location. The first drives north at 30mph, the second at 50mph to the west. How fast is the distance between them changing 4 hours into the drive?

Answer 1

distance = speed x time

Answer 2

therefore the distance the first driver goes is 30t , similarly the second driver goes 50t

Answer 3

now, the distance between them is a hypotenuse of right angle triangle, which can be found by pythagorus

Answer 4

Their distance at any time is \[\sqrt{x^{2}+y^2}\], where x is the first divers distance relative to the start, and y, the second divers...

Answer 5

d= sqrt ( 900t^2 + 2500t^2 ) = sqrt ( 3400t^2 ) = sqrt(3400) t

Answer 6

so would it be d(distance)/dt= Sqrt[(dN/dt)^2 + (dW/dt)^2]?

Answer 7

let D equal the distance , which is D= sqrt(3400) t from above


dD / dt = sqrt(3400) // doesnt depend on the time

Answer 8

which is what you would expect, none of the speed of the drivers are changing

Answer 9

okay... that makes sense... I thought there was more to it.