Question

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 tow-rope at the right moment she will glide to a stop near the 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 tow-rope when she reaches point A, where is she headed relative to the dock? Use an equation to desctibe path. ( Hint: she will travel in a straight line.)
b) if linda lets go of the tow-rope whe she reached point B, where is Linda headed relative to the dock?
c) If linda waits until point O, how close will her traectory be to the dock.

Answer 1

Linda's path relative to the dock changes depending on where she releases the tow-rope. At point A, she continues southeast towards the origin; at point B, she likely heads straight for the dock; at point O, she is already at the dock.

Step-by-step explanation:

The goal is to diagram the path Linda will travel relative to the dock if she releases the tow-rope at different points.

Point A: If Linda releases the tow-rope here, she will continue in a straight line towards the origin (0,0), which is the vertex of the parabolic path the boat takes. Since she's currently west and north of the origin, she would glide towards the southeast, potentially stopping short of the dock. Her path would be described by a straight line equation relative to her release point.

Point B: If she releases the tow-rope at this point, which would be on the parabolic path, she'd likely glide onto a path directly towards the dock, if timed correctly.

Point O: Assuming point O is the origin, if Linda lets go here, she will not cover any distance and will effectively be at the dock.

The straight-line paths Linda would travel when releasing the tow-rope can be described using vector addition and subtraction, similar to the method used for the example of the woman sailing a boat. The motion at point A can be seen as a straight line with a given direction and magnitude relative to the origin as the initial point.

Answer 2

The answer is c letting go of the towrope would make her fall or trip in the water, not to mention it would be very dangerous