Posted by Mr. goodstuff on Tuesday, January 17, 2012 at 11:53am.
A police cruiser, approaching a right –angled intersection from the north is chasing a speeding car that has turned the corner and is now moving straight east. When the cruiser is 0.6 mi north of the intersection and the car 0.8 mi to the east, the police determine with radar that the distance between them and the car is increasing at 20 mph. If the cruiser is moving at 60mph at the instant of measurement, what is the speed of the car?
calculus - Reiny, Tuesday, January 17, 2012 at 1:39pm
make a sketch
At a time of t hrs,
let the distance the police car is from the intersection be x miles
let the distance the speeding car is from the intersection be y miles
let the distance between them be d miles
d^2 = x^2 + y^2
2d dd/dt = 2x dx/dt + 2y dy/dt
d dd/dt = x dx/dt + y dy/dt
given: x = .6, y = .8 , dx/dt = -60 , dd/dt = 20
( I made dx/dt negative because the value of x is decreasing)
d^2 = .6^2 + .8^2 = 1
d = 1
1(20) = .6(-60) + .8dy/dt
20 + 36 = .8 dy/dt
dy/dt = 56/.8 = 70
The car was speeding at 70 mph
calculus - Freddie, Tuesday, January 17, 2017 at 11:51am
Answer This Question
More Related Questions
- Math - 1. 1. A police cruiser approaching a right-angled intersection from the ...
- Physics - a speeding car is driving at 120 km/h when it passes a police cruiser ...
- Calculus AB - A police car is chasing a suspect. The policemen is at point y=0.6...
- Physics - A car is speeding at 33.4 m/s. A police car starts in pursuit from ...
- calculus - A police car is driving northward, chasing a vehicle which has just ...
- maths - hi, need help in below problem. thanks. A cruiser which can steam at 48 ...
- calculus - A police cruiser hunting for a suspect pulls over and stops at a ...
- physics - Two cars are approaching a perpendicular intersection without a stop ...
- CALCULUS - A gas station stands at the intersection of a north-south road and an...
- Calculus - 4. A gas station stands at the intersection of a north-south road and...