Orienteering Compasses
Orienteering Compasses
Physics problem..Help please.? For {$keyword}

A scout troop is practicing its orienteering skills with map and compass. First they walk due east for 1.1 km. Next, they walk 40° west of north for 3.6 km. How far and in what direction must they walk to go directly back to their starting point?

b) direction in degrees east of south?

Start by sketching a picture.

Resolve each vector into an x-y pair, where positive x is due East and positive y is due North.

East is zero degrees. Directions will be measured as angle of rotaion counterslockwise from East. North is 90 degrees (measured from the positive x-axis)
1.1 km East = (1.1, 0)
3.6 kn @ 20 deg. West of North = (3.6 * cos(40 + 90), 3.6 * sin(40 + 90))
= (-2.31, 2.76)

Add:
(1.1, 0) + (-2.31, 2.76) = (-1.21, 2.76)

Distance back to the starting point
sqrt((-1.21)^2 + (2.76)^2)
= sqrt(9.0817)
= 3.01

This is where the picture is very helpful.
Direction
a = arctan(2.76/-1.21)
= arctan(-2.281)
= -66.3
That is measured relative to East, going counterclockwise. Add 90 degrees to get the angle measured East of South. -66.3 + 90 = 23.7 degres East of South.

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