Trigonometry

1. Ben is pulling on a tobaggan rope with a force of 250 newtons. The rope makes a 36 angle with the ground. What force is actually working to move the tobaggan to the right?

2. If a boat going 6 mi/hr in still water suddenly encounters a crosscurrent of 4 mi/hr, at what angle will the boat veer?

Thank you so much!


When pulling on an object with a force at some angle, the upward component is
sin(thetz)*force and the horizontal component is
cos(theta)*force

For the boat let's assume a simple position: it's going east and the crosscurrent is going north. The boat's velocity is
(6mi/hr,0) and the current's is (0,4mi/hr)
If the boat travels for one hour it will travel along some direction a distance 6mi and it will be 4mi north of where it started. Draw a right triangle with hypotenuse 6 and one leg =4 to correspond to the river's velocity. You should get sin(theta)=4/6. Do you see how to set this up now?

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