Acar travels down a highway at  25  m/s. an observer stands  100m from the highway. a) how fast is the distance from the observer to the car increasing when the car passes in front of the observer? (use decimal notation.) the rate is = (b) how fast is the distance increasing 10s later? (use decimal notation. give your answer to three decimal places.) the rate is =

Let x be the distance (in meters) along the road that the car has traveled andh be the distance (in meters) between the car and the observer.

Part (a):
Before the car passes the observer, we have ; after it passes, we have .
So at the instant it passes we have , given that varies continuously since the car travels at a constant velocity.
Therefore, the rate the distance from the observer to the car increasing when the car passes in front of the observer is 0m/s

Part (b):

By the Pythagorean Theorem, we have

Thus,


where: is the velocity at which the car is travelling.

Since the car travels at 25 m/s, so after 10 seconds, the distance (in meters) along the road that the car has traveled, x, is given by



and



Therefore,