SOLUTION: A particle undergoes two displacements. The first has a magnitude of 11 m and makes an angle of 76◦ with the positive x axis. The result after the two displacements is 8.

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Question 211112: A particle undergoes two displacements. The
first has a magnitude of 11 m and makes an
angle of 76◦ with the positive x axis.
The result after the two displacements is
8.7 m directed at an angle of 109 ◦ to the
positive x axis using counter-clockwise as the
positive angular direction (see the figure be-
low).
Find the magnitude of the second displace-
ment. Answer in units of m.
Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
The first displacement
.
delta x = 11 cos 76 = 2.661
delta y =11 sin 76 = 10.67
.
The final displacement
.
delta x = 8.7 cos 109 = -2.832
delta y = 8.7 sin 109 = 8.23
.
The second displacement
.
delta x = -2.832-2.661 = -5.493
delta y = 8.23 - 10.67 = -2.44
.
Magnitude of 2nd displacement = sqrt{ 5.493^2 +2.44^2 } = 6.01 m
.
A rough sketch helps visualize vectors
.