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

c = 13.5 m

Step-by-step 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 =
`√(25+100-(-57.4))`

c = 13.5 m