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
Let initial direction of motion be along
Since we are considering vectors, the second displacement vector makes an angle of
#:.# Angle of turn of the object#=360-240=120^@#
Now displacement
Resolving
#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#