Question

A truck starts off 151 miles directly north from the city of Hartville. It travels due east at a speed of 41 miles per hour. After travelling 36 miles, how fast is the distance between the truck and Hartville changing? (Do not include units in your answer, and round to the nearest hundredth.)

Answer 1

Answer:

9.51

Explanation:

The distance s is given by:

$s(t) = \sqrt{151^2 + (vt)^2}$

The change in distance is given by the time derivative of s:

$\frac{ds}{dt} = \frac{v^2t}{\sqrt{151^2 + (vt)^2}}$

For the time t you solve the equation of distance x for time:

$x = vt => t = \frac{x}{v}$

Plugging in for t:

$\frac{ds}{dt}(t=\frac{x}{v})=\frac{vx }{\sqrt{151^2 + x^2}}=9.51$