A treasure map directs you to start at a palm tree and walk due north for 9.0 m.

Question

A treasure map directs you to start at a palm tree and walk due north for 9.0 m. You are then to turn 90° and walk 13.0 m; then turn 90° again and walk 5.00 m. For each of the four possible locations of the treasure, give the distance from the palm tree and the direction, expressed as an angle measured counterclockwise from north. List the possible locations in counterclockwise (CCW) order, starting with the one which is closest to due east.
( ) m and ( )° (location closest to due east)
( ) m and ( )° (next location in the CCW direction)
( ) m and ( )° (next location in the CCW direction)
( ) m and ( )° (next location in the CCW direction)

Explanation / Answer

a) walk due north for 9.0 m, then due east for 13.0 m, then due northfor 5 m, total displacement = v[(9 + 5)^2 + 13^2 ] = 19.1 m, direction = tan-1(13/14) = 42.8 degrees east of north b) walk due north for 9.0m, then due west for 13.0 m, then due northfor 5 m, total displacement = v[(9.0 + 5)^2 + 13^2] = 19.1 m, direction = tan-1(13/14) = 42.8 degrees west of north c) walk due north for 15 m, then due east for 22 m, then due southfor 5 m, total displacement = v[(9.0 - 5)^2 + 13^2] = 13.6 m, direction = tan-1(13/4) = 72.8 degrees east of north d) walk due north for 15 m, then due west for 22 m, then due southfor 5 m, total displacement = v[(9.0m-5.0 m )^2 + 13^2 ] = 13.6 m, direction = tan-1(13/4.0) = 72.8 degrees west of north

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