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Chapter 3: Q2E (page 121)

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.

Short Answer

Expert verified

a. The total distance traveled is 1200 m .

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

Step by step solution

01

Determine total distance travel

A physical quantity is a material's physical property that can be quantified, such as mass, length, etc.

1 Block = 120 m.

For path B, the total distance traveled is:

= 4 blocks + 3 blocks + 3 blocks

= 10 blocks

=10脳20=1200m

Therefore, the total distance traveled by path B is 1200 m.

02

Determine the direction of displacement

The magnitude of the displacement from start to finish is:

d鈬赌=dx2+dy2=1Block2+3Block2

The direction of the displacement:

=1+9blocks=10blocks=10脳120m=3.162脳120m=379.4m

The direction of the displacement:

胃=tan-1dydx=tan-13block1block=tan-13=71.6掳NE

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

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Most popular questions from this chapter

(a) Repeat the problem two problems prior, but for the second leg you walk \(20.0{\rm{ m}}\) in a direction \(40.0^\circ \) north of east (which is equivalent to subtracting \({\rm{B}}\) from \({\rm{A}}\) 鈥攖hat is, to finding \({\rm{R'}} = {\rm{A}} - {\rm{B}}\)).

(b) Repeat the problem two problems prior, but now you first walk \(20.0{\rm{ m}}\) in a direction \(40.0^\circ \) south of west and then \(12.0{\rm{ m}}\) in a direction \(20.0^\circ \) east of south (which is equivalent to subtracting \({\rm{A}}\) from \({\rm{B}}\) 鈥攖hat is, to finding \({\rm{R''}} = {\rm{B}} - {\rm{A}} = - {\rm{R'}}\)). Show that this is the case.

(a) Another airplane is flying in a jet stream that is blowing at m/sin a direction south of east. Its direction of motion relative to the Earth is south of west, while its direction of travel relative to the air is south of west. What is the airplane鈥檚 speed relative to the air mass?

(b) What is the airplane鈥檚 speed relative to the Earth?

You drive \(7.50{\rm{ km}}\) in a straight line in a direction \(15^\circ \) east of north.

(a) Find the distances you would have to drive straight east and then straight north to arrive at the same point. (This determination is equivalent to find the components of the displacement along the east and north directions.)

(b) Show that you still arrive at the same point if the east and north legs are reversed in order.

The hat of a jogger running at constant velocity falls off the back of his head. Draw a sketch showing the path of the hat in the jogger鈥檚 frame of reference. Draw its path as viewed by a stationary observer.

Explain why a vector cannot have a component greater than its own magnitude.
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