actual speed of the red car is --- ft per second

Question

A police car is located 30 feet to the side of a straight road.

A red car is driving along the road in the direction of the police car and is 130 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 90 feet per second. How fast is the red car actually traveling along the road?

Answer 1

plot the diagram as a right triangle, with the origin where the red car will be closest to the police

the height of the triangle is 130. the base is 30. The hypotenuse squared = sum of the height squared plus

the base squared. h^2 = 130^2 + 30^2.

Let the distance from the red car to the origin be x

h^2 = x^2 + 30^2

h= about 133 feet

take the derivative, with respect to time, t

2hh' = 2xx'

2(133)(90) = 2(130)x'

solve for x'

266(90) = 260x'

x' = 266/260 times 90 ft/sec = slightly more than 90, about 92 feet per second

x' = dx/dt = the derivative of x with respect to t, how fast x changes as t changes

and usually a point or two off for wrong units. When you see 90+ speeds, with

police watching, that sounds too much like mph