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A boat is travelling due south at a speed of 53 miles per hour. If the boat started off 29 miles directly west of the city of Johnstown, how fast (in radians per hour) is the angle opposite the southward path changing when the boat has travelled 23miles? (Do not include units in your answer, and round to the nearest hundredth.)Provide your answer below:

Question

A boat is travelling due south at a speed of 53 miles per hour. If the boat started off 29 miles directly west of the city of Johnstown, how fast (in radians per hour) is the angle opposite the southward path changing when the boat has travelled 23miles? (Do not include units in your answer, and round to the nearest hundredth.)

Provide your answer below:

check_circleAnswer
Step 1

Let us suppose the distance of the boat towards south is y. Let the angle of the boat from the Johnstown be Ɵ. The distance in the west direction covered is 29 miles. To clear the picture, lets draw it. 

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Step 2

Use tan Ɵ and form a function Ɵ that depends on y as follows.

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Step 3

The speed of the boat in the south direction is 53 miles per hour which is nothing but dy/dt=53. Differentiate it with res...

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Tagged in

Math

Calculus

Derivative

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