On a calm lake, a floating leaf drifts steadily eastward. A person standing on a dock measures the leaf’s velocity to be 0.60m⋅s−1 east. A canoeist paddling in the same straight line observes the leaf to move 0.25m⋅s−1 west relative to the canoe.
Assume straight-line motion, constant speeds, and negligible wind.
(a) Determine the speed and direction of the canoe relative to the dock. Clearly indicate your sign convention and show all steps.
(b) Describe in words how your result in part (a) is consistent with the observations made by both the dock observer and the canoeist.
(c) The canoeist accelerates until the leaf is now observed to move 0.10m⋅s−1 west relative to the canoe. Calculate the canoe’s new speed relative to the dock.