Question

What is the resultant displacement of a dog looking for its bone in the yard, if the dog first heads 55° north of west for 10.0 m, and then turns and heads west for 5.00 m?

Answer 1

Answer:

c = 13.5 m

Explanation:

from the attached diagram, we can apply the cosine rule to get the resultant displacement (c) where

c = $\sqrt{a^{2}+b^{2}-2.a.b.cosθ}$

• from the diagram β = 55 degrees because they are alternate angles

         θ + β = 180  (sum of angles on a straight line )

         θ + 55 = 180

         θ = 180 - 55

        θ = 125 degrees

• c = $\sqrt{a^{2}+b^{2}-2.a.b.cosθ}$

            c = $\sqrt{5^{2}+10^{2}-2.5.10.cos125}$

           c =$\sqrt{25+100-(-57.4)}$

           c = 13.5 m