Question

A police car is located 50 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 140 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 70 feet per second. How fast is the red car actually traveling along the road?

Answer 1

Answer:74.33 feet per sec

Explanation:

Given

Police car is 50 feet side of road

Red car is 140 feet up the road

Distance between them is decreasing at the rate of 70 feet per sec

From figure

$x^2+y^2=z^2$

$z=\sqrt{140^2+50^2}$

z=148.66 feet

as the red car is moving

therefore its velocity magnitude is given by

$\frac{\mathrm{d} x}{\mathrm{d} t}$

$2x\times \frac{\mathrm{d} x}{\mathrm{d} t}+0=2z\frac{\mathrm{d} z}{\mathrm{d} t}$

$x\frac{\mathrm{d} x}{\mathrm{d} t}=z\frac{\mathrm{d} z}{\mathrm{d} t}$

$140\times \frac{\mathrm{d} x}{\mathrm{d} t}=148.66\times 70$

$\frac{\mathrm{d} x}{\mathrm{d} t}=74.33 feet\ per\ sec$