A truck starts off 180 miles directly east from the city of Hartville. It travels due south at a speed of 45 miles per hour. After travelling 49 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.)

Question
Asked Mar 22, 2019
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A truck starts off 180 miles directly east from the city of Hartville. It travels due south at a speed of 45 miles per hour. After travelling 49 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.)

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Expert Answer

Step 1

To find the rate of change of speed of the truck.

 

Let x be the distance between truck and Hartville changing, and let y be the distance between the Hartville and Hartville changing.

Step 2

The current situation can be represented as follows.

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Step 3

Obtain the distance between the Hartville and Hartville changing by using the Pythagoras theorem as y^2 = x^2 + 180^2.

 

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Math

Calculus