Wind is blowing at 273 Degrees and 112N. You must reach the island within 5 minu

Question

Wind is blowing at 273 Degrees and 112N. You must reach the island within 5 minutes, otherwise you will be caught are returned to your prison walls.

The island is located at the coordinates (5000, 0) using the polar coordinate system. You are currently situated in the position (0,0).

The boats mass, including you is 145 kg.

what is the force to paddle and direction to paddle ? Please let me know if i need to conver the 273 degrees to something else ? I know i have to find acceleration and then F=ma formula to get F of paddle. Now how do i find the direction ?

Explanation / Answer

You need to row in that direction so that the net force due to the wind gets cancelled and your net velocity is straight towards the island. You start from rest and you need to cover a distance of 5000 m so, 5000 = .5*a*(5*60)^2 where a is the acceleration of the boat a = 0.1111 N Since angle of the wind is making an angle of (273-270) with the horizontal = 3 degrees. Force of wind in horizontal direction = 112*cos(3) = 111.8465 N Force in vertical= 112*sin(3) = 5.861627N Force applied the boat in horizontal = 111.8465 N In vertical = 0.111*145 - 5.861627 =10.088 N Net force = 112.300555 N ( vector sum of the above two) Direction of paddel = tan(theta) = 111.8465/ 10.088 theta =84.84614 degrees from the vertical

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