1.1+ Speed in various frames. Consider the situation shown on page 5. In addition to the home, the bicycle, and the car shown in the figures, a motorcycle drives to the right at 50 miles/hour relative to the Earth. a. In the frame of the bicycle, what is the speed of the motorcycle? b. In the frame of the motorcycle, what is the speed of the motorcycle?

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1.1+ Speed in various frames. Consider the situation shown on page 5. In addition to
the home, the bicycle, and the car shown in the figures, a motorcycle drives to the right
at 50 miles/hour relative to the Earth.
25
a. In the frame of the bicycle, what is the speed of the motorcycle?
b. In the frame of the motorcycle, what is the speed of the motorcycle?
Transcribed Image Text:1.1+ Speed in various frames. Consider the situation shown on page 5. In addition to the home, the bicycle, and the car shown in the figures, a motorcycle drives to the right at 50 miles/hour relative to the Earth. 25 a. In the frame of the bicycle, what is the speed of the motorcycle? b. In the frame of the motorcycle, what is the speed of the motorcycle?
Earth's frame
O
Bicycle's frame
5 mph
5 mph
This sketch shows the speeds relative to the Earth or, as we will often say, "speeds
observed from the Earth's reference frame." (We could also say "speeds from my
frame" or "speeds from the sidewalk's perspective" or "speeds from the sidewalk's
frame" or "speeds in the sidewalk's frame." All of these phrases have the same
meaning.)
The Paradox of the Mirror
But I'm not the only person who can observe this scene. The cyclist is just as good
a person as I am. From the point of view of the cyclist, the car is still moving, but it's
not drawing away from him as quickly as it's drawing away from me; in fact, it's mov-
ing at 15 miles/hour as observed from the bicycle's reference frame. Meanwhile, from
the point of view of the cyclist, the home is drawing away from the bicycle. In fact,
it is moving left at 5 miles/hour (or, what is the same thing, right at -5 miles/hour).
Here's a sketch of the situation from the cyclist's point of view:
Ò
20 mph
0 mph
5
15 mph
Transcribed Image Text:Earth's frame O Bicycle's frame 5 mph 5 mph This sketch shows the speeds relative to the Earth or, as we will often say, "speeds observed from the Earth's reference frame." (We could also say "speeds from my frame" or "speeds from the sidewalk's perspective" or "speeds from the sidewalk's frame" or "speeds in the sidewalk's frame." All of these phrases have the same meaning.) The Paradox of the Mirror But I'm not the only person who can observe this scene. The cyclist is just as good a person as I am. From the point of view of the cyclist, the car is still moving, but it's not drawing away from him as quickly as it's drawing away from me; in fact, it's mov- ing at 15 miles/hour as observed from the bicycle's reference frame. Meanwhile, from the point of view of the cyclist, the home is drawing away from the bicycle. In fact, it is moving left at 5 miles/hour (or, what is the same thing, right at -5 miles/hour). Here's a sketch of the situation from the cyclist's point of view: Ò 20 mph 0 mph 5 15 mph
Expert Solution
Step 1

Relative Speed:

The relative speed of body A with respect to a frame is defined as the speed observed from that frame.

For an object A moving with velocity vA with respect to frame S and an object B moving with velocity vB with respect to the same frame, the relative speed of body A with respect to the frame of body B is given as,

vAB=|vA-vB|

 

Assume the left direction to be negative and the right direction to be positive.

 

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