I need help for part B Problem 16 Part A Ships A and B leave port together. For

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I need help for part B

Problem 16 Part A Ships A and B leave port together. For the next two hours, ship A travels at 23 mph in a direction 39 west of north while ship B travels 23 °east of north at 27 mph What is the distance between the two ships two hours after they depart? Express your answer using two significant figures R= 52 miles Submit My Answers Give Up Correct Part B What is the speed of ship A as seen by ship B? Express your answer using two significant figures mph Submit My Answers Give Up Incorrect; Try Again; 13 attempts remaining Provide Feedback

Explanation / Answer

Part A:

Ship A makes an angle of (90 – 39)=51° with West. And after 2 hours its distance is 46 mph. Hence its components are (-46*cos(51°), 46*sin(51°))

Similarly for ship B, the components after 2 hours are (54*cos(67°), 54*sin(67°))

Hence, the distance between them is given by:

s² = {54*cos(67°) + 46*cos(51°)}² + {54*sin(67°) - 46*sin(51°)}²

    = {21.1 + 29.0}^2 + {49.7 – 35.7}^2

     = 2510.01 + 196 = 2706.01

=> s = 52.02 mile.

So, the distance between the ships after two hours = 52.02 miles.

Part B:

Speed of the ship A as seen by ship B = 52.02 / 2 = 26.01 mph

The direction is given by tan() = {-54*sin(67°) + 46*sin(51°)}/{-54*cos(67°) - 46*cos(51°)}

=> tan() = (35.7-49.7) / (-21.1 – 29.0) = -14 / -50.1 = 0.279

=> = 15.6 deg

Hence, speed of ship A as viewed from ship B, is 26.01 mph and in the direction of (90-15.6) = 74.4° West of North.

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