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**1. The preserver upstream. 2. The preserver downstream **

Suppose you and a pair of life preservers are floating down a swift river, as shown. You wish to get to either of the life preservers for safety. One is 3 meters downstream from you and the other is 3 meters upstream from you. Which can you swim to in the shortest time? Ch 3-1 Thanks to John Clement and Charlie Camp. 1. The preserver upstream. 2. The preserver downstream 3. Both require the same.

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Suppose you and a pair of life preservers are floating down a swift river, as shown. You wish to get to either of the life preservers for safety. One is 3 meters downstream from you and the other is 3 meters upstream from you. Which can you swim to in the shortest time? Ch 3-1 Thanks to John Clement and Charlie Camp. Answer: 3 To get a grip on this, pretend that you are in a swimming pool on a fast-moving ocean liner. If both life preservers are the same distance from you in the pool, swimming toward either would take the same time. The speed of the ocean liner through the water makes no difference, just as it makes no difference to people playing shuffleboard or billiards. Can you see that in the flowing river, you’re like a person in a pool aboard a moving ocean liner—that swimming toward either preserver takes the same time! 1. The preserver upstream. 2. The preserver downstream 3. Both require the same.

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**1. Track A. 2. Track B. 3. Both reach the end at the same time.**

Tracks A and B are made from pieces of channel iron of the same length. They are bent identically except for a small dip near the middle of Track B. When the balls are simultaneously released on both tracks as indicated, the ball that races to the end of the track first is on Ch 3-2 1. Track A. 2. Track B. 3. Both reach the end at the same time.

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**1. Track A. 2. Track B. 3. Both reach the end at the same time.**

Tracks A and B are made from pieces of channel iron of the same length. They are bent identically except for a small dip near the middle of Track B. When the balls are simultaneously released on both tracks as indicated, the ball that races to the end of the track first is on Ch 3-2 Answer: 2 The ball to win the race is the ball having the greatest average speed. Along each track both balls have identical speeds—except at the dip in Track B. Instantaneous speeds everywhere in the dip are greater than the flat part of the track. Greater speed in the dip means greater overall average speed and shorter time for a ball on Track B. If your answer was 3, you may have been influenced by realizing that both balls finish at the same speed. Quite true, but not in the same time. Although the speed gained when going down the dip is the same as the speed lost coming out of the dip, average speed while in the dip is greater than along the flat part of the track. If this seems tricky, it’s the classic confusion between speed and time. 1. Track A. 2. Track B. 3. Both reach the end at the same time.

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**1. 60 km/h. 2. 80 km/h. 3. 90 km/h. 4. faster than the speed of light.**

A motorist wishes to travel 40 kilometers at an average speed of 40 km/h. During the first 20 kilometers, an average speed of 40 km/h is maintained. During the next 10 kilometers, however, the motorist averages only 20 km/h. To drive the last 10 kilometers and average 40 km/h, the motorist must drive 1. 60 km/h km/h km/h. 4. faster than the speed of light. Ch 3-3

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**1. 60 km/h. 2. 80 km/h. 3. 90 km/h. 4. faster than the speed of light.**

A motorist wishes to travel 40 kilometers at an average speed of 40 km/h. During the first 20 kilometers, an average speed of 40 km/h is maintained. During the next 10 kilometers, however, the motorist averages only 20 km/h. To drive the last 10 kilometers and average 40 km/h, the motorist must drive 1. 60 km/h km/h km/h. 4. faster than the speed of light. Ch 3-3 Answer: 4 You would have to travel at an infinite speed and finish the last 10 kilometers in zero time to attain an average speed of 40 km/h! Why? Because you have 1 hour to make the trip, and your 1 hour is up at the 30-km point. You spent 1/2 hour to the halfway point, 20 km, and another 1/2 hour when you averaged 20 km/h over that 10 km stretch. So you’d have to cover the entire 40 km in 1 hour—that means the last 10 km in no time at all. Be careful in averaging speeds like you average distances. Speed involves distance and time. Be sure to consider time in problems that involve speed!

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**1. more 2. less 3. the same time as with no wind?**

An airplane makes a straight back-and-forth round trip, always at the same airspeed, between two cities. If it encounters a mild steady tailwind going, and the same steady headwind returning, will the round trip take: Ch 3-5 1. more 2. less 3. the same time as with no wind?

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**1. more 2. less 3. the same time as with no wind?**

An airplane makes a straight back-and-forth round trip, always at the same airspeed, between two cities. If it encounters a mild steady tailwind going, and the same steady headwind returning, will the round trip take: Ch 3-5 Answer: 1 The windy trip will take more time, as any numerical example will show. Suppose the cities are 600 km apart, and the airspeed of the plane is 300 km/h (relative to still air). Then time each way with no wind is 2 hours. Roundtrip time is 4 hours. Consider a 100 km/h tailwind going, so groundspeed is (300 + 100) km/h. Then the time is , or 1 hour and 30 minutes. Returning groundspeed is (300 – 100) km/h, and the time is , or 3 hours. The windy round trip takes 4.5 hours—longer than with no wind at all. Since this is one of those “greater than, equal to, or less than” questions, use exaggerated values—like windspeed equaling airspeed. Then it’s easy to see the plane cannot make the return trip with such a headwind. As windspeed approaches airspeed, roundtrip time approaches infinity. For any windspeed, roundtrip time is always greater than with no wind. 1. more 2. less 3. the same time as with no wind?

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