Ms. C goes water-skiing one sunny afternoon. After skiing for 15 min, he signals to the driver of the boat to take him back to the dock. The driver steers the boat toward the dock, turning in a parabolic path as it nears. If Ms. C lets go of the towrope at the right moment, he will glide to a stop near the dock. Let the vertex of the parabola traveled by 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. Be sure to explain your reasoning and use diagrams to support your answers.

a) If Ms. C lets go of the tow rope when he reaches point A, where is he headed to the dock? Use an equation to describe the path. [Hint: He will travel in a straight line].

b. If Ms. C lets go of the towrope when he reaches point B, where is Ms. C headed relative to the dock?

c. If Ms. C waits until point C, how close will his trajectory be to the dock?

d. At what point should Ms. C release the towrope to head straight for the dock?

e. What assumptions have you made?

Skier Boat Dock C