Posted by MILEY on Thursday, April 8, 2010 at 2:21am.
A gas station stands at the intersection of a northsouth road and an eastwest road. A police car is traveling towards the gas station from the east, chasing a stolen truck which is traveling north away from the gas station. The speed of the police car is 100 mph when it is 3 miles from the gas station. At the same time the truck is 4 miles from the gas station going 80 mph. At this moment:
a. Is the distance between the car and the truck increasing or decreasing? How fast?
b. Repeat part a) if the truck is going 70 mph instead of 80 mph

CALCULUS  Damon, Thursday, April 8, 2010 at 6:58am
a = distance apart = (x^2 + y^2)^.5
at present a = 5 miles (3,4,5 triangle)
da/dt = .5 (x^2+y^2)^.5 (2x dx/dt + 2 y dy/dt)
if dx/dt = 100
dy/dt = +80
then
da/dt = (.5/5)(2*3*100 + 2*4*80)
= (.1)(600 + 640)
= +4
the truck is making a getaway at the moment.
You can do it for the truck doing 70 mph. I suspect the truck will be losing then.

CALCULUS  miley, Thursday, April 8, 2010 at 11:26am
SO B is 4. which is decreasng
Answer This Question
Related Questions
 Calculus  4. A gas station stands at the intersection of a northsouth road and...
 Trigonometry  A car traveling at a constant rate due east passes an interstate ...
 physic  Nora’s car is run out of gas and she noticed that a gas station is just...
 FREE BODY DIAGRAM calculus  A car is traveling north towards an intersection at...
 physics  A car that starts out 250 meters east of a gas station at time zero ...
 Calculus AB  A police car is chasing a suspect. The policemen is at point y=0.6...
 physics  On a safari, a team of naturalists sets out toward a research station ...
 Physics  I need major help with this please!!! On a safari, a team of ...
 Physics  On a safari, a team of naturalists sets out toward a research station ...
 Physics  While traveling to school at 27 m/s your car runs out of gas 15 hm ...
More Related Questions