The purpose of the following
exercise is to examine the motion of a projectile using a graphical method
and to practice vector operations. Present
your solutions as described in the instructions below.
The following information is given about the projectile. Positive velocities are to the right and up.
Horizontal 
Vertical 
x_{o} = 0 
y_{o} = 0 
v_{ox}= 0.750 m/s 
v_{oy} = 0.000 m/s 
a_{x} = 0.00 m/s² 
a_{y} = 9.80 m/s² 
A. Equations of motion

Write the
complete dvat equations for v_{x}, v_{y}, x, and y.
See Table 41 in the text.
 Substitute into the equations quantities that
are zero and rewrite the 4 equations in simplified form.
B. Data: Use the 4 simplified equations to fill in values in a
table like the following.
t
(s) 
x
(m) 
y
(m) 
v_{x}
(m/s) 
v_{y}
(m/s) 
0.000 
0.000 
0.000 
0.750 
0.000 
0.050 




0.100 




0.150 




0.200 




C. Graphical construction: For the following, accurate measurement and construction is important in order to obtain good results.

The graph paper provided for this class is ruled in major divisions of centimeters. Plot the 5 positions of the projectile above at
actual scale. That is, one centimeter on the graph paper will represent one realworld centimeter
of distance. Turn the paper in portrait orientation in order to fit the five points on the grid.

At each position, draw vectors to represent the
horizontal and vertical components of the velocity. Draw all vectors
to a scale such that 1.0 cm on the graph paper represents 0.50 m/s. Note that this is a distancetospeed scale, since you’re using distances to represent the magnitude of the velocity.
 Use the graphical method of vector addition to construct the velocity vector, v, for each pair of velocity components. See this animation in order to see how your vectors may appear. (You
can change the launch angle to 0, but note that the velocity
magnitudes are different than given for this problem.)
D. Acceleration vector: The average acceleration vector can be found as the vector difference of two
velocity vectors divided by the time interval between them. That is,
.

Select two such velocity vectors and construct their difference
in the unused lower lefthand corner of your graph paper. Select the initial velocity vector as one of the two.
Label each vector in your vector difference drawing. See Fig. 314
on page 64 of your text to review how to construct the difference of
two vectors.
 Once you've constructed the vector difference, measure its length and use
the scale factor to convert to m/s. Then divide by the time interval to find the magnitude of the average acceleration. State both the magnitude and direction of the average acceleration vector.
E. Question: Does the value of average acceleration that you calculated depend on what two velocity vectors you choose? Explain. 