# calculus

posted by uGinn

One bicycle is east of an intersection , and it is travelling towards the intersection of 9 miles per hour. at the same time a second bicycle is south of the intersection , and it is travelling away from the intersection at the rate of 10 miles per hour. Is the distance between the bicycles increasing or decreasing when the first is 4 miles east and the second is 4 miles south of the intersection? at what rate?

1. bobpursley

let u be the distance of the first bike
let v be the distance of the second bike

u^2+v^2=x^2
given du/dt=-9
and dv/dt=10

2x dx/dt=2u du/dt + 2v dv/dt
dx/dt= (u du/dt +v dv/dt)/x
now solve for dx/dt when u=4,v=4, and du/dt and dv/dt given as above.
if it is increasing, dx/dt will be +

2. Anonymous

e = distance east
s = distance south
h = hypotenuse, what we want

at start
e = 4
s = 4
de/dt = -9
ds/dt = +10
h = 4 sqrt 2

h^2 = e^2 + s^2
2 h dh/dt = 2 e de/dt + 2 s ds/dt

4 sqrt 2 (dh/dt) = 4 (-9) + 4 (+10)

sqrt 2 (dh/dt) = +1
dh/dt = 1/sqrt 2 = +.707 miles/hour

obviously 10 is bigger than 9 :)

## Similar Questions

1. ### Physics - Momentum of cars at intersection

Two cars of identical mass are approaching the same intersection, one from the south and the one from the west. They reach the intersection at the same time and collide. The cars lock together and move away at an angle of 22deg counterclockwise …
2. ### AP CALC

Two roads intersect at right angles. At a certain moment, one bicyclist is 8 miles due NORTH of the intersection traveling TOWARDS the intersection at a rate of 16 miles/hour. A second bicyclist is 10 miles due WEST of the intersection …
3. ### calculus

A police car is driving northward, chasing a vehicle which has just taken a right turn at an intersection, and is travelling due west. When the police car is 600 yards south of the intersection, and the car is 800 yards east of the …
4. ### calculus

A team has been working to convert diesel-powered cars to run just as efficiently on used cooking oil! They want to compare the mileage and speed of their prototype with that of the diesel-powered car. The prototype is 100 meters south …
5. ### Calculus

A team has been working to convert diesel-powered cars to run just as efficiently on used cooking oil! They want to compare the mileage and speed of their prototype with that of the diesel-powered car. The prototype is 100 meters south …
6. ### 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 …
7. ### Calculus

Two cars leave an intersection at the same time. Car X is travelling East at 50 km/hr and Car Y is travelling South at 60 km/hr. Find the rate at which the cars are separating after 30 minutes.
8. ### Calculus

Two cars leave an intersection at the same time. Car X is travelling East at 50 km/hr and Car Y is travelling South at 60 km/hr. Find the rate at which the cars are separating after 30 minutes.
9. ### Calculus

Two cars leave an intersection at the same time. Car X is travelling East at 50 km/hr and Car Y is travelling South at 60 km/hr. Find the rate at which the cars are separating after 30 minutes. I want its complete solution
10. ### college math

two cars are approaching an intersection one is 3 miles south of the intersection and is moving at a constant speed of 20 miles per hour. at the same time the other car is 4 miles east of the intersection and is moving at the constant …

More Similar Questions