Question

1. a rover on mars is being tracked by the command center back at nasa. if the initial position of the rover is 74.5 m from the origin (base) and its final position is -8.3 m. what is the displacement of the rover?

δx = x_f - x_i
δx = -8.3 m - 74.5 m = -82.8 m

1. a bird flies 1585 meters west and then 771 m east.

a) what is the total distance traveled by the bird?
x_west + x_east = 1585 m + 771 m = 2356 m
b) what is the displacement of the bird? (hint: take west to be the negative direction and east to be the positive direction)
δx = x_f - x_i
δx = -1585 m - 771 m = -2356 m

1. a hiker is initially 1.5 miles east of base camp (which is the origin). the hiker walks until they are completely exhausted and end up a distance of 6.7 miles west of base camp. what is the hiker’s displacement? (hint: take east to be the negative direction and west to be the positive direction).

δx = x_f - x_i
δx = 6.7 miles - (-1.5 miles) = 8.2 miles

1. study the diagram below, showing the route that nellie nerinx took when she drove her car to the corner market. nellie starts at her house (the origin, location a), rides along the bold path shown and finishes at the market (location b). each square in the diagram represents 1 km. use the diagram in answering the next two questions:

nellie drove a total distance of 31 km.

1. which of the following correctly states nellie’s displacement if her house is located at point a, the origin:

a) 0 km
b) 3 km
c) 3 km to the right
d) 3 km to the left
e) 31 km
f) 31 km to the right
g) 31 km to the left

1. a fishing boat leaves its dock (this location is the origin) and travels 3.5 km north. then, the boat turns around and travels 18.8 km south. finally, the boat turns around again and travels 5.1 km north again.

a) what is the total distance traveled by the boat?
δt = t_f - t_i
b) what is the displacement of the boat? (hint: call north the positive direction and south the negative direction. add all the parts of the motion, keeping track of direction)

Explanation:

Question 13a: Total Distance Traveled by the Boat

Step 1: Identify the distances traveled

The boat travels 3.5 km North, 18.8 km South, and 5.1 km North.

Step 2: Sum the distances

To find the total distance, we add the magnitudes of each distance traveled. So, total distance \( d = 3.5 + 18.8 + 5.1 \).
First, calculate \( 3.5 + 18.8 = 22.3 \). Then, \( 22.3 + 5.1 = 27.4 \).

Step 1: Assign signs to directions

Let North be positive (\( + \)) and South be negative (\( - \)). The displacements are: \( +3.5 \) km (North), \( -18.8 \) km (South), and \( +5.1 \) km (North).

Step 2: Sum the displacements

Displacement \( \Delta x = 3.5 + (-18.8) + 5.1 \).
First, \( 3.5 - 18.8 = -15.3 \). Then, \( -15.3 + 5.1 = -10.2 \) km. The negative sign indicates the direction is South.

Answer:

The total distance traveled by the boat is \( \boldsymbol{27.4} \) km.

Question 13b: Displacement of the Boat