A football player runs the pattern given in the drawing by the three displacement vectors , , and . The magnitudes of these vectors are A = 4.00 m, B = 15.0 m, and C = 18.0 m. Using the component method, find the (a) magnitude and (b)direction of the resultant vector + + . Take to be a positive angle

Answer 1

A, DUE NORTH from start position
B, 90 degrees East
C, 37 degrees south east

Answer 2

R = 4m[90o] + 15m[0o] + 18m[-37o].

X = 4*Cos90 + 15*Cos0 + 18*Cos(-37o) =
0 + 15 + 14.4 = 29.4 m.

Y = 4*sin90 + 15*sin0 + 18*sin(-37) =
4 + 0 -10.8 = -6.8 m.

a. sqrt(X^2+Y^2)=sqrt(29.4^2+(-6.8)^2) =
30.2 m. = Magnitude.

b. Tan A = Y/X = -6.8/29.4 = -0.23129.
A = -13.3o = 13.3o S. of E.=346.7o CCW.
= Direction.