4. The speed for vehicles is typically given in reference to the medium it travels on or through. For example, a car with a top speed of 180 mph is going that speed relative to the ground [in the "ground frame"], while a ship with a top speed of 30 mph is going that speed relative to the water [in the "water frame"], and an airplane with a top speed of 700 mph is going that speed relative to the air [in the "air frame"]. The velocities of these 1.5 km objects becomes more complicated when the medium they move through is itself moving, so a plane at top speed subject to a 100 mph tail wind still travels at 700 mph relative to the air, but is going 800 mph relative to the ground. Suppose, when spring arrives, you want to kayak from Bard to the opposite shore of the Hudson, which is 1.5 km due west if you travel the shortest distance across. Your kayaking speed, relative to the water is 1.0 m/s, but the river is flowing due south at 0.5 m/s relative to the shore. 0.5 m/s (shore frame) A) If you paddle due west in the river's frame, what is your speed relative to the shore? B) How long does it take you to reach the other shore (noting you don't go straight across)? C) Suppose you paddle in a direction at l m/s relative to the water that ensures you go the shortest distance across the river, what is your speed relative to the shore? D) How long does it take you to reach the other shore using this method?
4. The speed for vehicles is typically given in reference to the medium it travels on or through. For example, a car with a top speed of 180 mph is going that speed relative to the ground [in the "ground frame"], while a ship with a top speed of 30 mph is going that speed relative to the water [in the "water frame"], and an airplane with a top speed of 700 mph is going that speed relative to the air [in the "air frame"]. The velocities of these 1.5 km objects becomes more complicated when the medium they move through is itself moving, so a plane at top speed subject to a 100 mph tail wind still travels at 700 mph relative to the air, but is going 800 mph relative to the ground. Suppose, when spring arrives, you want to kayak from Bard to the opposite shore of the Hudson, which is 1.5 km due west if you travel the shortest distance across. Your kayaking speed, relative to the water is 1.0 m/s, but the river is flowing due south at 0.5 m/s relative to the shore. 0.5 m/s (shore frame) A) If you paddle due west in the river's frame, what is your speed relative to the shore? B) How long does it take you to reach the other shore (noting you don't go straight across)? C) Suppose you paddle in a direction at l m/s relative to the water that ensures you go the shortest distance across the river, what is your speed relative to the shore? D) How long does it take you to reach the other shore using this method?
Physics for Scientists and Engineers, Technology Update (No access codes included)
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Chapter39: Relativity
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![4. The speed for vehicles is typically given in reference to the
medium it travels on or through. For example, a car with a top
speed of 180 mph is going that speed relative to the ground [in
the "ground frame"], while a ship with a top speed of 30 mph is
going that speed relative to the water [in the "water frame"], and
an airplane with a top speed of 700 mph is going that speed
relative to the air [in the "air frame"]. The velocities of these
1.5km
objects becomes more complicated when the medium they
move through is itself moving, so a plane at top speed subject to
a 100 mph tail wind still travels at 700 mph relative to the air,
but is going 800 mph relative to the ground. Suppose, when
spring arrives, you want to kayak from Bard to the opposite shore of the Hudson, which is 1.5 km
due west if you travel the shortest distance across. Your kayaking speed, relative to the water is
0.5 m/s
(shore frame)
1.0 m/s, but the river is flowing due south at 0.5 m/s relative to the shore.
A) If you paddle due west in the river's frame, what is your speed relative to the shore?
B) How long does it take you to reach the other shore (noting you don't go straight across)?
C) Suppose you paddle in a direction at 1 m/s relative to the water that ensures you go the
shortest distance across the river, what is
your speed relative to the shore?
D) How long does it take you to reach the other shore using this method?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1fed7a52-65d8-44f4-988f-6c762cda0c09%2Fd1d7e9e7-062e-41bf-a2be-f2e034c840e3%2Fchsj92q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. The speed for vehicles is typically given in reference to the
medium it travels on or through. For example, a car with a top
speed of 180 mph is going that speed relative to the ground [in
the "ground frame"], while a ship with a top speed of 30 mph is
going that speed relative to the water [in the "water frame"], and
an airplane with a top speed of 700 mph is going that speed
relative to the air [in the "air frame"]. The velocities of these
1.5km
objects becomes more complicated when the medium they
move through is itself moving, so a plane at top speed subject to
a 100 mph tail wind still travels at 700 mph relative to the air,
but is going 800 mph relative to the ground. Suppose, when
spring arrives, you want to kayak from Bard to the opposite shore of the Hudson, which is 1.5 km
due west if you travel the shortest distance across. Your kayaking speed, relative to the water is
0.5 m/s
(shore frame)
1.0 m/s, but the river is flowing due south at 0.5 m/s relative to the shore.
A) If you paddle due west in the river's frame, what is your speed relative to the shore?
B) How long does it take you to reach the other shore (noting you don't go straight across)?
C) Suppose you paddle in a direction at 1 m/s relative to the water that ensures you go the
shortest distance across the river, what is
your speed relative to the shore?
D) How long does it take you to reach the other shore using this method?
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