Find the resultant vector made by 115 km at 80 degrees and 85 km at 15 degrees

[KatieJo]

I have worked and worked at this problem and it is just not clicking. It is now that I wish geometry would have made sense to me.

I am trying to find the resultant vector made by 115 km at 80 degrees and 85 km at 15 degrees. I have been using the graphing method my teacher showed me. I want to use law of cosines or law of sines, but I have two unknowns. The answer is probably right under my nose.

If you could help me understand this problem, it would be greatly appreciated! Thank you for your help!

Katie Jo

 

[Mozart]

First find the Horizontal components, and the vertical components of each vector. Then you can add them to begin getting your new vector. After you have your new magnitutde you will need to find the angle it creates. You can just do the inverse function of tan If you want to find the angle. Oh and don't forget to give the directions. For example here is a random vector 200 Newtons [E 30 degrees N] or you can just up down left right.

 

[HallsofIvy]

Assuming you mean "80 degrees to the horizontal" and "15 degrees to the horizontal" (just saying "80 degrees" doesn't mean anything without a reference), then you can do it using the cosine law. If you were to continue the first vector's line, it still makes 80 degrees to the horizontal and so 80- 15= 65 degrees to the second vector. That means the inner angle between the two vectors is 180- 65= 115 degrees. You have a triangle with two sides of length 115 and 85 km and an angle of 115 degrees between them. The length of the resultant vector (opposite side) is given by x²= 115²+ 85²- 2(115)(85)cos(115).

Once you have that you can use the sine law to find the angles.