Displacement Problem: Solve 5th & 3rd Turn

[takando12]

Homework Statement

A man starts from "O" moves 500m , turns by 60° and moves 500m again again turns by 60° and moves 500m and so on. Find the displacement after 1) 5th turn 2) 3rd turn (assume each turn is clockwise from the man's point of view.

Homework Equations

The Attempt at a Solution

I tried drawing a diagram and I think it looks like an equilateral triangle with the man going through the same path after every 3rd turn. And so after some counting I concluded that the answers are 1) 500m and 2) 0m . But the correct answers are 500 and 1000 m respectively. Is my method wrong? How do i solve this?

 

[SammyS]

Homework Statement

A man starts from "O" moves 500m , turns by 60° and moves 500m again again turns by 60° and moves 500m and so on. Find the displacement after 1) 5th turn 2) 3rd turn (assume each turn is clockwise from the man's point of view.

Homework Equations

The Attempt at a Solution

I tried drawing a diagram and I think it looks like an equilateral triangle with the man going through the same path after every 3rd turn. And so after some counting I concluded that the answers are 1) 500m and 2) 0m . But the correct answers are 500 and 1000 m respectively. Is my method wrong? How do i solve this?

I think you're turning by 120° .

 

[takando12]

I think you're turning by 120° .

oh. I took the angle with respect to the backward path. Stupid mistake. Anyway does it turn out to be a hexagon now? I am able to get the right answers.
Thanks a lot sir.

 

[SammyS]

oh. I took the angle with respect to the backward path. Stupid mistake. Anyway does it turn out to be a hexagon now? I am able to get the right answers.
Thanks a lot sir.

Yes, a hexagon.