# Find the distance she walks

## Homework Statement

A woman walks 132 m in the direction 41° east of north, then 170 m directly east. Find (a) the magnitude and (b) the angle (from due east) of her final displacement from the starting point. (c) Find the distance she walks.

??

## The Attempt at a Solution

N displacement of leg 1 = (cos41) x 132m., = 99.62m.
E displacement of leg 1 = (sin 41) x 132m., = 86.6m.

Total N displacement = 99.62m.
Total E displacement = (170 + 86.6) = 256.6m.

a) Magnitude = sqrt. (99.62^2 + 256.6^2), = 275.26 m.
b) Sin L = (99.62/275.26), so L = 22.22 degrees, N of E.
c) (132 + 170) = 302 m.

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Mark44
Mentor

## Homework Statement

A woman walks 132 m in the direction 41° east of north, then 170 m directly east. Find (a) the magnitude and (b) the angle (from due east) of her final displacement from the starting point. (c) Find the distance she walks.

??

## The Attempt at a Solution

N displacement of leg 1 = (cos41) x 132m., = 99.62m.
E displacement of leg 1 = (sin 41) x 132m., = 86.6m.
41 deg. E of North is an angle of 49 deg counterclockwise from the positive x-axis. Use 49 deg in your calculations above.
Total N displacement = 99.62m.
Total E displacement = (170 + 86.6) = 256.6m.

a) Magnitude = sqrt. (99.62^2 + 256.6^2), = 275.26 m.
b) Sin L = (99.62/275.26), so L = 22.22 degrees, N of E.
c) (132 + 170) = 302 m.

wait I don't understand

Mark44
Mentor

What don't you understand? When you're calculating the components of vectors, the angles need to be measured from the pos. x-axis. The heading 41 deg. E of North is measured from the y-axis.

so it would be like this

sin(49) x 132=99.62?

Mark44
Mentor

That would be the vertical component of the first leg of her walk.

yeah i don't get sorry :(

Mark44
Mentor

You are doing your calculations with an angle measured from the y-axis. I'm doing calculations with an angle measured from the x-axis. We're both getting the same answers for the vertical component (N displacement) and horizontal component (E displacement).

I get a slightly different angle, using the N and E displacements and arctan, getting 21.2 deg N of E.