NAME__________________________________DATE________PERIOD______



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.

[pic]

a) Write parametric equations that express the distance the Little Old Lady traveled.

x1 = ______________________

y1 = ______________________

[pic]

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 = [pic] 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)

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A 17-3

A 17-3

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[pic]

Maria catches Paul ______

hours after she left home at

a distance of ___________

miles.

[pic]

[pic]

[pic]

[pic]

A 17-3

[pic]

[pic]

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