Question

A boy runs 10.3 blocks North, 6.1 blocks
Northeast, and 5 blocks West.
Determine the length of the displacement
vector that goes from the starting point to his
final position.

Determine the direction of the displacement
vector. Use counterclockwise as the positive
angular direction, between the limits of −180◦
and +180◦ measured from East.
Answer in units of ◦
.

Answer 1

D = 10.3[90o] + 6.1[45] + 5[180].

X = 10.3*Cos90 + 6.1*Cos45 + 5*Cos180 =
0 + 4.31 - 5 = -0.69 Blocks.

Y = 10.3*sin90 + 6.1*sin45 + 5*sin180 =
10.3 + 4.31 + 0 = 14.61 Blocks.

D = sqrt(X^2+Y^2) = sqrt((-0.69)^2 + 14.61^2) = 14.6 Blocks.

Tan A = Y/X = 14.61/-0.69 = -87.3o =
87.3o N. of W. = 92.7o CCW.