Quiz Lesson 3 Unit 2
1. Each year at the annual Park Street block party, there is a beanbag toss contest. The goal
of the contest is to toss the beanbag so that it lands between two red lines that are drawn
on the street. The first red line is 12 feet from the tossing line and the second is 13 feet
from the tossing line.
Courtney tosses a beanbag so that it travels on the path modeled by the following
parametric equations.
x = 18.5t cos 65˚ + 1
y = 18.5t sin 65˚ – 16t2 + 3
a. Describe where the beanbag is when Courtney lets go of it.
b. How fast is the beanbag moving when Courtney lets go of it?
c. What is the maximum height the beanbag reaches?
d. How long is the beanbag in the air?
e. Is Courtney’s toss too long or too short? Explain your reasoning.
f. What angle of release should Courtney use so that the beanbag will land between the
two red lines?
2. Giancarlo’s rear bicycle tire has a trademark (bright red dot) on its extreme outer edge.
The radius of the tire is 13.5 in., and the trademark is initially located at the “3 o’clock”
position.
a. Make a sketch of the wheel as described on a rectangular coordinate system. Let the horizontal
axis represent the ground and the vertical axis contain the center of the wheel. Mark the origin O,
the trademark M, and the center of the wheel C.
b. Giancarlo makes the wheel revolve at 4 radians per second. Write parametric equations that
model the location of the trademark on the turning wheel at time t seconds.
c. How far above the ground is the trademark at t = 2.3?
3. Write parametric equations for each of the following.
a. A vertical line through the point (4, –5)
b. A circle with radius 10 and center at (2, –5)
c. An ellipse with center at the origin and crossing the x-axis at ±10 and the y-axis at ±6