# CALCULUS

posted by .

A gas station stands at the intersection of a north-south road and an east-west 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 -

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 -

SO B is -4. which is decreasng

## Similar Questions

1. ### Calculus

4. A gas station stands at the intersection of a north-south road and an east-west 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 …
2. ### Physics

While traveling to school at 27 m/s your car runs out of gas 15 hm from the nearest gas station. If the station is 16m above your current elevation, how fast will the car be going when it reaches the gas station?
3. ### Calculus AB

A police car is chasing a suspect. The policemen is at point y=0.6 (north of an intersection) and the suspect is at point x=0.8 (east of the intersection). The police car is traveling at 60mph. Their radar gun reads that the suspect's …
4. ### physics

A car that starts out 250 meters east of a gas station at time zero and passes it in 10 seconds. Draw your graph showing the car traveling at least 250 meters past the gas station to the West.
5. ### Physics

On a safari, a team of naturalists sets out toward a research station located 4.0 km away in a direction 42° north of east. After traveling in a straight line for 2.3 km, they stop and discover that they have been traveling 30° north …
6. ### Physics

I need major help with this please!!! On a safari, a team of naturalists sets out toward a research station located 6.9 km away in a direction 42° north of east. After traveling in a straight line for 2.1 km, they stop and discover …
7. ### FREE BODY DIAGRAM calculus

A car is traveling north towards an intersection at 60mph at the same time a truck is headed east toward the same intersection at 45mph. Find the rate of change of the distance between the car and truck when the car is 3 miles south …
8. ### physics

On a safari, a team of naturalists sets out toward a research station located 5.54 km away in a direction 47.9 ° north of east. After traveling in a straight line for 1.29 km, they stop and discover that they have been traveling 24.6 …
9. ### Trigonometry

A car traveling at a constant rate due east passes an interstate exit that is 1.0 mile from a gas station. The gas station is S50°E of the exit. After the car has traveled for 2.0 minutes, its bearing to the gas station is S55°W. …
10. ### physic

Nora’s car is run out of gas and she noticed that a gas station is just 125 feet away the incline road. She decided to push the car up a 14 degree inclined with a force of 250 N to get to the gas station. Determine how much work …

More Similar Questions