Calculus
posted by Vivi .
Car A traveling southward towards Point P at 45 mi/hr. Car B is traveling east away from P at 30mi/hr. AT the instant when the distance AP is 60 mi and PB is 80 mi, what is the rate of change of distance AB?

Calculus 
Steve
We have a nice 345 triangle at the moment in question, so AB = 100
If we let x and y be the distances of the two cars (B and A) then the distance d=AB is
d^2 = x^2 + y^2
2d dd/dt = 2x dx/dt + 2y dy/dt
so, when x=80 and y=60, d=100, and we have
100 dd/dt = 80(30) + 60(45)
dd/dt = 3
Respond to this Question
Similar Questions

math
distance = rate x time or d = r*t car traveling 40 mi/hr goes 40 mi/hr x 1.5 hrs head start or 60 miles head start. Let t = time bus and car travel. car travels distance of r*t = 40*t. Car already had 60 mi head start. Total distance … 
Physics
Car A is traveling at 84 km/h while Car B is traveling at 58 km/h. What is the relative velocity of Car A to Car B if they both are traveling in the same direction? 
Physics
Car A is traveling at 84 km/h while Car B is traveling at 58 km/h. What is the relative velocity of Car A to Car B if they both are traveling in the same direction? 
Physics
The instant a traffic light turns green a car that has been waiting at the light starts forward with a constant acceleration of 10 ft/s^2. At the same instant a truck traveling at a constant 30 ft/s overtakes and passes the car. 1. … 
Calculus
4. 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 … 
CALCULUS
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 … 
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 … 
PHYSICSURGENT HELP
A stationary police car emits a sound of frequency 1200 Hz that bounces off of a car on the highway and returns to the police car with a frequency of 1250 Hz. The police car is right next to the highway, so the moving car is traveling … 
Calculus
"Two cars are traveling along perpendicular roads, car A at 40mph, car B at 60mph. At noon, when car A reaches the intersection, car B is 90miles away, and moving toward it. At 1PM the distance between the cars is changing at what … 
Physics
A 1500 kg car traveling at 100 km/h west collides with a 1200 kg car traveling east at 85 km/h. The heavier car slows to 25 km/h after the collision. How fast is the lighter car traveling after the two cars collide?