Question

Mr. Letourneau is flying his broom stick parallel to the ground. He undergoes two consecutive displacements. The first is $100km10degrees$ west of north, and the second is $120km50degrees$ east of north. What is the magnitude of the broom stick's displacement? (in km)

• A. $190$
  
• B. $191$
  
• C. $91$
  
• D. $82$
  

Answer 1

The correct option is B $191$

The displacement are schematically shown in figure.

From this figure we can see that the angle between the first and the second displacement is $120°$. Then from the triangle based on the first second and net displacements, we can find the magnitude of the net displacement (cosine formula)

$s=\sqrt{{100}^2+{120}^2-2\times 100\times 120\times \cos \left(120°\right)}$

$=191km$