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ID: 1778812 • Letter: A
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asterin -MP Secure | https://session.masteringphysics.com/myct/itemView?assignmentProblemID-86280210 F17-MP3 Problem 4.53 Resources previous | 6 or 8 | next » Problem 4.53 Part A A kayaker needs to paddle north across a 100-m-wide harbor. The tide is going out, creating a tidal current that flows to the east at 2.0 m's. The kayaker can paddle with a speed of 3.0 m/s In which direction should he paddle in order to travel straight across the harbor 56.3 west of north O 48.2 ° west of north 41.8" west of north O 33.7 west of north Submit My Answers Give Up Part B How long will it take him to cross? Express your answer with the appropriate units. ValueUnits Submit My Answers Give Up 2:55 PM 015/2017Explanation / Answer
The first part is vector arithmetic. The sum should be due N. One part is the tide at 2 m/s E, the other is the paddling at 3 m/s in an unknown direction.
Add together the X and Y components
Tx = 2, Ty = 0
Px = ?, Py = ?
Rx = 0, Ry = ?
P² = Px² + Py²
3² = Px² + Py²
Rx = Tx + Px
0 = 2 + Px
Px = -2
3² = 2² + Py²
Py = 2.236
angle P = arctan 2.236/2 = 48.2 deg N of W which is 41.8 deg W of N
To get across the 100 meters, only his Y component counts, the x component counters the tide.
100 m / 2.236 m/s = 44.7 sec
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