NAME______DATE______PERIOD______
WORKSHEET – HORIZONTAL MOTION PROBLEMS
1. The “Little Old Lady from Pasadena” drove her car 300 miles from Dallas to Lubbock at a rate of 80 miles per hour. Her good friend “ Surfer Boy”, drove his car from Dallas to Lubbock at a rate of 50 miles per hour (you know how laid back surfers are). The two leave at the same time and follow a linear path.
a) Write parametric equations that express the distance the Little Old Lady traveled.
x1 = ______
y1 = ______
b) Write parametric equations that express the distance the surfer
traveled.
x2 = ______
y2 = ______
c) Enter the equations into your calculator and set an appropriate viewing window.
Window: Tmin ______x-min ______
Tmax ______x-max ______
T step ______y-min ______
y-max ______
Answer the following questions from your graph.
d) After 2 hours , who is ahead and by how much? ______
e) Who arrives first and how much sooner ? ______
f) If the surfer starts out 150 miles closer to Lubbock than the Little Old Lady, how will the original equations change?
x1 = ______x2 = ______
y1 = ______y2 = ______
g) Under these new conditions, who arrives first and how much sooner ?
______
2. Paul, who runs cross country, can run at an average velocity of 6 miles per hour. Two hours after he leaves home on his morning run, his mother needs to give him a message. She sends his sister, Maria, on her bike to give him the message. Maria can ride at an average velocity of 15 mph. Write parametric equations to model this situation and determine from the graph when she will catch up to Paul.
x1 = ______x2 = ______
y1 = ______y2 = ______
Window: Tmin ______x-min ______
Tmax ______x-max ______
T step ______y-min ______
y-max ______
3. Sherry leaves Columbus, Ohio on a to Dallas traveling 50 mph.
Five hours later, Larry leaves Dallas in a to Columbus which is traveling at 70 mph.
Columbus and Dallas are 950 miles apart.
a) Write parametric equations to illustrate the trips. Let x be the distance from Dallas.
x1 = ______x2 = ______
y1 = ______y2 = ______
Window: Tmin ______x-min ______
Tmax ______x-max ______
T step ______y-min ______
y-max ______
b) Will Sherry arrive in Dallas before Larry arrives in Columbus? ______
Sherry arrives in ______hours. Larry arrives in ______hours.
c) If Larry leaves 6 hours after Sherry instead of the original 5, who arrives first? ______
Sherry arrives in ______hours. Larry arrives in ______hours.
Non-Calculator. Write the parametric equations of the following graphs.
4. x = ______5. x = ______
y = ______y = ______
6. For the parametric equations: x = 4-2t y = for t in [0, 6]
a) Make a table of values
b) Draw the graph and show the orientation.
c) Write the rectangular equation.
a) b) c)