Posted by **Mike** on Thursday, June 13, 2013 at 8:51pm.

A car leaves an intersection traveling west. Its position 5 sec later is 22 ft from the intersection. At the same time, another car leaves the same intersection heading north so that its position 5 sec later is 27 ft from the intersection. If the speed of the cars at that instant of time is 15 ft/sec and 5 ft/sec, respectively, find the rate at which the distance between the two cars is changing. (Round your answer to one decimal place.)

ft/sec

- Calculus -
**Reiny**, Thursday, June 13, 2013 at 11:48pm
let the distance of the west-bound car from the intersection be x

let the distance of the north-bound car from the intersection be y

and let the distance between them be d

d^2 = x^2 + y^2

2d dd/dt = 2x dx/dt + 2y dy/dt

**d dd/dt = x dx/dt + y dy/dt**

when x=22, y=27 , dx/dt = 15 ft/sec , dy/dt = 5 ft/sec

and d^2 = 22^2 + 27^2 = 1213

d = √1213

√1213 dd/dt = 22(15) + 27(5) = 465

dd/dt = 465/√1213 = appr 13.4 ft/s

## Answer this Question

## Related Questions

- calculus - A car leaves an intersection traveling east. Its position t sec later...
- FREE BODY DIAGRAM calculus - A car is traveling north towards an intersection at...
- PHYSICS - a car traveling at a constant velocity of 30 m/sec passes an ...
- PHYSICS - A car traveling at a constant velocity of 30.0 m/sec passes an ...
- Physics - Momentum of cars at intersection - Two cars of identical mass are ...
- Math - A car is heading east toward an intersection at the rate of 40 mph. A ...
- Math - A car is heading east toward an intersection at the rate of 40 mph. A ...
- Calculus Maxima/Minima - An automobile traveling at the rate of 30 ft/sec is ...
- Calculus - A team has been working to convert diesel-powered cars to run just as...
- physics - Two cars are approaching a perpendicular intersection without a stop ...