Calculating Displacement of a Grizzly Bear: Homework Solution

[deaky220]

Homework Statement

14.In wandering, a grizzly bear makes a displacement of 1563 m due west, followed by a displacement of 3348m in a direction 32.0degrees north of west. What are a)the magnitude b) the direction of the displacement needed for the bear to return to its starting point? Specify the direction relative to due east.(pg 4 of notes)

Homework Equations

mag=squareroot of x^2 + y^2

The Attempt at a Solution

I took the x and y components of both vectors A and B. added them up took square root of x^2 and y^2 to get 4438 m. then took the inverse tan of 4438/1563 and got 70.6 degrees East. 2 questions i had was if my formula is correct in that the Magnitude = either the square root of x^2 + y^2 or is it just x^2 + y^2 and for the direction do i take the inverse tan of the x and y components like x over y or do i take the inverse tan of opp/adj which is 4438/1563? Thanks to anyone who can help me check my answer I have no where else to look.

 

[Redbelly98]

Yes, you take the square root of x²+y².

For the angle, take the inverse tan of
y-component / x-component
(That's opposite/adjacent sides, if you draw a right triangle)

And the direction can't be eastward ... the bear travels west and/or north only.

p.s. Welcome to Physics Forums!

 

[gabbagabbahey]

Homework Statement

14.In wandering, a grizzly bear makes a displacement of 1563 m due west, followed by a displacement of 3348m in a direction 32.0degrees north of west. What are a)the magnitude b) the direction of the displacement needed for the bear to return to its starting point? Specify the direction relative to due east.(pg 4 of notes)

Homework Equations

mag=squareroot of x^2 + y^2

The Attempt at a Solution

I took the x and y components of both vectors A and B. added them up took square root of x^2 and y^2 to get 4438 m. then took the inverse tan of 4438/1563 and got 70.6 degrees East. 2 questions i had was if my formula is correct in that the Magnitude = either the square root of x^2 + y^2 or is it just x^2 + y^2 and for the direction do i take the inverse tan of the x and y components like x over y or do i take the inverse tan of opp/adj which is 4438/1563? Thanks to anyone who can help me check my answer I have no where else to look.

Your method looks fine, but your answers are incorrect. What did you get for the total x-component and the total y-compnent and what exactly did you do to get them?