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Chapter 3: Q1E (page 121)

Find the following for path A in Figure,

(a) the total distance traveled, and

(b) the magnitude and direction of the displacement from start to finish.

The various lines represent paths taken by different people walking in a city. All blocks are120 mon a side.

Short Answer

Expert verified

a. The total distance traveled is 480 m.

b. The magnitude and direction of the displacement from start to finish is 379.4 m & 71.6°NE

Step by step solution

01

Vector definition

A vector is a quantity that has both magnitude and direction. Displacement, velocity, force, torque, and other vector quantities are examples.

02

Determine the total distance

a) Block = 120 m

For path A, the total distance traveled is:

=4blocks=4×120m=480m

Therefore the total distance traveled by path A is 480 m.

03

Determine the direction of displacement

b) The magnitude of the displacement from start to finish is:

d⇀=dx2+dy2=1block2+3block2

d⇀=1+9blocks=10blocks=10×120m=3.162×120m=379.4m


The direction of the displacement:

θ=tan-1dydx=tan-13block1block=tan-13=71.6°NE

Therefore the magnitude and direction of the displacement from start to finish is 379.4 m &71.6°NE

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Most popular questions from this chapter

Find the following for path B in Figure:

(a) the total distance traveled, and

(b) the magnitude and direction of the displacement from start to finish.

The various lines represent paths taken by different people walking in a city. All blocks are m on a side.


Solve the following problem using analytical techniques: Suppose you walk 18.0mstraight west and then 250.0mstraight north. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements and , as in Figure, then this problem asks you to find their sum R=A+B.)

The two displacements and add to give a total displacement having magnitude and direction .

Note that you can also solve this graphically. Discuss why the analytical technique for solving this problem is potentially more accurate than the graphical technique.

A cloud of dirt falls from the bed of a moving truck. It strikes the ground directly below the end of the truck. What is the direction of its velocity relative to the truck just before it hits? Is this the same as the direction of its velocity relative to ground just before it hits? Explain your answers.

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(a) In what direction would the ship have to travel in order to have a velocity straight north relative to the Earth, assuming its speed relative to the water remains 7.00m/s?

(b) What would its speed be relative to the Earth?
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