Chapter 15.5, Problem 1aTH

Reference frame of boat B:

Complete the upper diagram at right by drawing and labeling boats A, B, and the kayak at their positions at time $t_i$as measured in the frame of boat B.

In the space at lower right, draw and label vectors for the initial position, the final position, and the displacement of the kayak in the frame of boat B.

In the frame of boat B, is the speed of the kayak greater than, less than, or equal to the speed of boat A? Explain.

To determine

The position of boat A, B and kayak at time $t_{\text{f}}$ and the initial position, final position and displacement of the kayak and compare the speed of kayak and boat A in frame of boat B.

Explanation of Solution

Introduction:

A frame of reference is a combination of coordinate $\left(x,y,z\right)$ of an object which describes the position of the object with respect to the coordinate system and clock which is used to measure time. If one or more coordinate of an object change with time, then the object is said to be in motion.

In frame of boat B, the speed of boat B is zero. Boat A and kayak will move in the left direction in frame of boat B.

The final position of boat A, boat B and in frame of boat B is shown in figure 1.

  

  Figure 1

The initial position, final position and displacement of kayak are shown in figure 2.

  

  Figure 2

The displacement of kayak is more than the displacement of boat A for same interval of time. So, the speed of kayak is greater than the speed of boat A in frame of boat B.

Conclusion:

Therefore, the position of boat A, B and kayak at time $t_{\text{f}}$ and the initial position, final position and displacement of the kayak is shown in figure 1 and 2 respectively. The speed of kayak is greater than the speed of boat A in frame of boat B.