A deer runs 88 feet to the east, then turns and runs at an angle of 11 ° north of west for 127 feet. What is the magnitude of the deer's resultant vector?

Answer 1

Draw a figure!

Your instructor may have intended you to solve this problem using vector addition for which you will need to obtain the co-ordinates of a line through the origin at an angle of 11 degrees and length 127. You can do this using some simple trig, namely the co-ordinates are x=127 cos 11 degrees and y=127 sin 11 degrees. Then use vector addition and the magnitude of a vector to answer the question.

Alternatively the answer can be obtained using the law of cosines with and angle of 169 degrees and sides of 88 and 127.

Answer 2

The first vector is 88 feet east. The second vector is 127sin11=24.2 feet north and 127cos11=124.7 feet west. Assume East & North are + then West & South are -. The difference between the first and second vector line is 88-124.7= -36.7 feet East and 24.2 feet North. The magnitude of that vector is sqrt((-36.7)^2+24.2^)= 44.0 feet.