Question

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

Answer 1

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`