Quiz C Unit 2 Lesson 2
Name___________________________
1. Jamie is looking for a hidden treasure. The first step in a set of directions to the treasure
is to begin at the old oak tree and travel 700 yards on a path with direction 300˚. Consider a
standard coordinate system with the old oak tree at the origin.
a.
What are the coordinates of Jamie’s location after she has traveled on this path for 500
yards?
b.
Suppose that Jamie jogs at 150 yards a minute on the indicated path. What are the
coordinates of her location after she has traveled for t minutes?
c.
Use your coordinates in part b to determine the actual coordinates after she has traveled 3
minutes.
d.
Jack is looking for the same treasure. The first step in a set of directions that he found
says to begin at the old oak tree and travel 750 yards on a path with direction 320˚.
Remember the first step in Jamie's set of directions to the treasure was to begin at the old
oak tree and travel 700 yards on a path with direction 300˚. How far away from each
other after 450 yards?
2.
Consider the following three position vectors.
a = (5, 10)
b = (12, –6)
c has length 11 and direction 145˚
a.
Determine the coordinate form of 3a 2(b – a ) .
b.
Which of the three vectors has the greatest magnitude? show your work.
c.
Use the dot product to find the measure of the angle between a and b. Show your work.
3.
Write parametric equations for each of the following paths.
a.
A horizontal linear path through the point (-5, 10)
b.
A linear path that makes a 60˚ angle with the positive x-axis
4.
Consider the following pair of parametric equations:
x = 2t – 4
y=t+1
a.
On the coordinate grid below, draw a graph of this pair of parametric equations for
0 ≤ t ≤ 3. Show your table of values in the space to the right of the graph.
b.
Determine the y-intercept of the segment you drew in Part a. For what value of t will
the y-intercept occur? Show your work.
c.
Does the point (.8, 3.3) lie on the graph of this pair of parametric equations? Show
your work.