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Chapter 2: Q. 57 (page 62)
A lead ball is dropped into a lake from a diving board 5.0 m
above the water. After entering the water, it sinks to the bottom with a constant velocity equal to the velocity with which it hit the water. The ball reaches the bottom 3.0 s after it is released. How deep is the lake?
The lake isdeep.
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Larry leaves home at 9:05 and runs at a constant speed to the lamp post seen in FIGURE EX2.3. He reaches the lamppost at 9:07, immediately turns, and runs to the tree. Larry arrives at the tree at 9:10. a. What is Larry鈥檚 average velocity, in m/min, during each of these two intervals? b. What is Larry鈥檚 average velocity for the entire run?
FIGURE EX2.32 shows the acceleration graph for a particle that starts from rest at t = 0 s. What is the particle鈥檚 velocity at t = 6 s?
A cheetah spots a Thomson鈥檚 gazelle, its preferred prey, and
leaps into action, quickly accelerating to its top speed of 30 m/s, the highest of any land animal. However, a cheetah can maintain this extreme speed for only 15 s before having to let up. The cheetah is 170 m from the gazelle as it reaches top speed, and the gazelle sees the cheetah at just this instant. With negligible reaction time, the gazelle heads directly away from the cheetah, accelerating at for 5.0 s, then running at constant speed. Does the gazelle escape? If so, by what distance is the gazelle in front when the cheetah gives up?
A particle鈥檚 acceleration is described by the function ax = 110 - t2 m/s2 , where t is in s. Its initial conditions are x0 = 0 m and v0x = 0 m/s at t = 0 s. a. At what time is the velocity again zero? b. What is the particle鈥檚 position at that time?
As a science project, you drop a watermelon off the top of the Empire State Building, 320 m above the sidewalk. It so happens that Superman flies by at the instant you release the watermelon. Superman is headed straight down with a speed of 35 m/s. How fast is the watermelon going when it passes Superman?
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