PHYS 111 – General Physics I Summer 2009
Please, attach this form to your homework. Don’t forget to specify your name and section.
Name: _______ HOMEWORK #1 – Due Friday, May 22
Consider three coplanar vectors CBA
, , , with magnitudes A =
2.69, B = 1.80, C = 2.50, and directions given as in the adjacent
figure by θ
A
= 68.2°, θ
B
= 33.5°, θ
C
= 36.9°. The vectors are to be
graphically and analytically solved into the vector resultant
3
R B A C
= − +
a) [2] Use the tail-to-tip technique on the adjacent grid to sketch
the vector
R
graphically.
b) [3] Calculate the x and y-components of each of the vectors
, , .
A B C
Then write the vectors in terms of their components
and unit vectors
ˆ
x
,
ˆ
y
(e.g.,
ˆ ˆ
x y
A A x A y
= +
).
c) [3] Using the components of
CBA
, ,
, calculate the magnitude of vector
R
and its direction
(counterclockwise angle
θ
) with respect to the negative direction of x-axis.
d) [2] On a separate piece of paper, with the arbitrarily scaled xy-axes, draw the vectors
CBA
, ,
using the
respective components (a big, neat diagram). Make sure that the vectors are drawn to scale. Represent vector
R
on the figure, preferably with a different color. Compare with the qualitative result from part a) for
consistency.
B: The <Animations> button on our webpage links to several Flash animations. Note that the application G01 models the
addition of three coplanar vectors, so you may want to check it out to see how your vector R is supposed to look like.
θ
A
A
B
θ
C
x
C
θ
B
y
A
B
C
