An object moves 1m in a straight line displacement a and changes direction moves another 1m in straight line displacement b and then ends up 1m from the starting point. Through which angle did it turn? Find the magnitude of a-b

1 Answer
Jul 30, 2018

This is what I get

Explanation:

It is given that the three points; initial location, intermediate location and the final location make an equilateral triangle of side #1\ m#.

Let initial direction of motion be along #+x#-axis

Since we are considering vectors, the second displacement vector makes an angle of #180+60=240^@# with the positive #x#-axis.

#:.# Angle of turn of the object #=360-240=120^@#

Now displacement #veca=hati\ m#
Resolving #vecb# in to its components we get

#vecb=(-cos60hati-sin60hatj)\ m#
#:.veca-vecb=hati-(-cos60hati-sin60hatj)#
#=>veca-vecb=(1+cos60)hati+sin60hatj#

Inserting values of angles we get

#veca-vecb=1.5hati+sqrt3/2hatj#
#=>|veca-vecb|=sqrt((1.5)^2+(sqrt3/2)^2)#
#=>|veca-vecb|=sqrt3\ m#