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**1. of y, exactly. 2. slightly lower than y. 3. slightly higher than y.**

A projectile is fired from a horizontal spring-loaded gun aimed directly (along the line of sight) at a distant bull’s eye. Because of the pull of gravity during flight, the projectile misses and hits a point at distance y beneath the bull’s eye. To hit the bull’s eye, the gun should be aimed along a line of sight above the bull’s eye, a vertical distance Ch 10-4 Thanks to Ken Ford. 1. of y, exactly. 2. slightly lower than y. 3. slightly higher than y.

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**1. of y, exactly. 2. slightly lower than y. 3. slightly higher than y.**

A projectile is fired from a horizontal spring-loaded gun aimed directly (along the line of sight) at a distant bull’s eye. Because of the pull of gravity during flight, the projectile misses and hits a point at distance y beneath the bull’s eye. To hit the bull’s eye, the gun should be aimed along a line of sight above the bull’s eye, a vertical distance Ch 10-4 Thanks to Ken Ford. Answer: 3, slightly higher than y, for two reasons. First, when the gun is tipped upward, the horizontal component of velocity is less. So there’s a slightly longer time of flight and the projectile falls a greater vertical distance. Second, depending on the mass of the projectile and strength of the spring, the emerging velocity is less in the raised position because the spring not only pushes the projectile, but lifts it somewhat against gravity. 1. of y, exactly. 2. slightly lower than y. 3. slightly higher than y.

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Consider the pair of identical blocks about to be simultaneously released from rest. Block A is completely free, and Block B is attached to one end of a massive chain, the other end held as shown. When dropped, both blocks hit the floor below—a vertical distance equal to the length of the chain. Which block hits first? Ch 10-8 Thanks to Dave Kagan and Alan Kott. 1. Block A 2. Block B

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Consider the pair of identical blocks about to be simultaneously released from rest. Block A is completely free, and Block B is attached to one end of a massive chain, the other end held as shown. When dropped, both blocks hit the floor below—a vertical distance equal to the length of the chain. Which block hits first? Ch 10-8 Thanks to Dave Kagan and Alan Kott. Answer: 2 Block B hits the floor first. Notice that the race isn’t between Blocks A and B, but between A and the end part of the B-chain system, which isn’t in free-fall because one end is fastened to the post. So it doesn’t accelerate at g like Block A. The B-chain’s center of mass, initially closer to the floor, accelerates less than g. But acceleration of its “free” end increases in fall, surpassing g—like the tip of a falling pole accelerates more than g when it rotates to the ground. 1. Block A 2. Block B

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