PowerPoint® Lectures for

General Physics I and Engineering I – Physics Department, UAEU

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Chapter 3

Motion in Two or

Three Dimensions

Lecture 3 Sec. 3.5

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Learning Goals

• To identify the velocity of a moving body as seen from

different frames of reference.

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3.5 Relative Velocity

Relative velocity: The velocity of a moving body seen by a

particular observer (velocity relative to that observer).

A frame of reference is a coordinate system plus a time scale.

Consider 4 planes in an

airshow moving together with

speed v.

What is the velocity of one of the planes

with respect to the ground?

What is the velocity of one of the planes

with respect to another plane?

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Relative velocity in One Dimension

• The position of P relative to

reference frame B is 𝑥𝑃/𝐵.

• The position of the train (B)

relative to reference frame A is 𝑥𝐵/𝐴.

• The x-position of P relative to

frame A (stationary) is

𝑥𝑃/𝐴 = 𝑥𝐵/𝐴 + 𝑥𝑃/𝐵

• The x-velocity of P relative to

frame A (stationary) is 𝑑𝑥𝑃/𝐴

𝑑𝑡

𝑉𝑃/𝐴−𝑥 = 𝑉𝐵/𝐴−𝑥 + 𝑉𝑃/𝐵−𝑥

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Example 3.13

You drive north at constant speed

of 88 km/hr.

A truck in the other lane moving

south at constant speed of

104 km/hr. Find

a) The truck’s velocity relative to

you.

b) Your velocity relative to the

truck.

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Example

A girl, moving at 8 𝑚/𝑠 on rollerblades, and a boy is moving behind her

at 5 𝑚/𝑠. The girl tosses a ball backward toward the boy, giving it a

speed of 12 𝑚/𝑠 relative to her. What is the speed of the ball relative to

the boy?

8 m/s

12 m/s

5 m/s

Observer

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Relative velocity in Two or Three Dimensions

• We extend relative velocity to two or

three dimensions by using vector

addition to combine velocities.

𝑟 𝑃/𝐴 = 𝑟 𝐵/𝐴 + 𝑟 𝑃/𝐵

• The velocity of P relative to frame A

(stationary) is 𝑑𝑟 𝑃/𝐴

𝑑𝑡

𝑉𝑃/𝐴 = 𝑉𝐵/𝐴 + 𝑉𝑃/𝐵

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Example 3.14

An airplane’s compass indicates that it is headed north, and its airspeed

indicator shows that it is moving through the air at 240 km/hr. If there is a

100 km/hr wind from west to east, what is the velocity of the plane

relative to the earth?

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Test your understanding

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A 0.14-km wide river flows with a uniform speed of 4.0 m/s toward the east.

It takes 20 s for a boat to cross the river to a point directly north of its

departure point on the south bank. What is the speed of the boat relative to

the water?

Example

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Q3 The pilot of a light airplane with an airspeed of 200 km/h

(𝑉𝑃/𝑊) wants to fly due west. There is a strong wind of

120 km/h blowing from the north (𝑉𝑊/𝐸).

If the pilot points the nose of the airplane north of west so

that her ground track is due west, what will be her ground

speed?

A. 80 km/h

B. 120 km/h

C. 160 km/h

D. 180 km/h

E. It would impossible to fly due west in this situation.

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Summary

Relative velocity: When a body P moves in a reference frame

B with 𝑉𝑝/𝐵, and the velocity of B relative to A is 𝑉𝐵/𝐴. Then

the velocity of P relative to the stationary reference frame A

is: 𝑉𝑝/𝐴 = 𝑉𝑝/𝐵 + 𝑉𝐵/𝐴