TASK

The Water Skier: Where's the Dock?

Water-skiing is a popular summertime

activity across Canada. A skier, holding onto

a towrope, is pulled across the water by a

motorboat.

Linda goes water-skiing one sunny

afternoon. After skiing for 15 min, she

signals to the driver of the boat to take her

back to the dock. The driver steers the boat

toward the dock, turning in a parabolic path

as it nears. If Linda lets go of the towrope

at the right moment, she will glide to a stop

near the dock.

Skier

Boat

A

B

Dock

Let the vertex of the parabola travelled by

the boat be the origin. The dock is located

30 m east and 30 m north of the origin. The boat begins its approach to the

dock 30 m west and 60 m north of the origin.

a) If Linda lets go of the towrope when she reaches point A, where is she

headed relative to the dock? Use an equation to describe the path.

(Hint: She will travel in a straight line.)

b) If Linda lets go of the towrope when she reaches point B, where is Linda

headed relative to the dock?

c) If Linda waits until point C, how close will her trajectory be to the dock?

d) At what point should Linda release the towrope to head straight for the

dock?

e) What assumptions have you made?

f) To make this situation more realistic, what additional information would

you need? Create this information, and solve part d) using what you have

created.

As you work through the task, be sure to explain your reasoning and use

diagrams to support your answers.