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Amusement Park Divers: Speed and Physics Analysis
Chapter 2, Problem 2.83(choose chapter or problem)
Visitors at an amusement park watch divers step off a platform 21.3 m (70 ft) above a pool of water. According to the announcer, the divers enter the water at a speed of 56 mi/h (25 m/s). Air resistance may be ignored. (a) Is the announcer correct in this claim? (b) Is it possible for a diver to leap directly upward off the board so that, missing the board on the way down, she enters the water at 25.0 m/s? If so, what initial upward speed is required? Is the required initial speed physically attainable?
Questions & Answers
QUESTION:
Visitors at an amusement park watch divers step off a platform 21.3 m (70 ft) above a pool of water. According to the announcer, the divers enter the water at a speed of 56 mi/h (25 m/s). Air resistance may be ignored. (a) Is the announcer correct in this claim? (b) Is it possible for a diver to leap directly upward off the board so that, missing the board on the way down, she enters the water at 25.0 m/s? If so, what initial upward speed is required? Is the required initial speed physically attainable?
ANSWER:Step 1 of 3
(a) Suppose the final velocity of the diver is v. Now we know that the initial velocity \(u=0 \mathrm{~m} / \mathrm{s}\), the acceleration due to gravity is \(g=9.8 m / s^{2}\) and the distance travelled is \(h=21.3 \mathrm{~m}\).
Now from the dynamics we know that
\(\begin{array}{l} v^{2}=u^{2}+2 g h=0 \mathrm{~m} / \mathrm{s}+2 g h=2 g h \\ \Rightarrow v=\sqrt{2 g h}=\sqrt{2\left(9.8 m / s^{2}\right)(21.3 \mathrm{~m})}=20.4 \end{array}\)
Hence the velocity at which the diver will enter the water is 20.4 m/s.
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Amusement Park Divers: Speed and Physics Analysis
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Step into the thrilling world of amusement park divers as we explore the physics behind their jaw-dropping stunts. Diving from a platform 21.3 meters (70 feet) above a pool of water, we investigate the announcer's claim that divers enter the water at a speed of 56 miles per hour (25 meters per second). We'll also uncover the possibility of divers leaping directly upward to achieve a specific water entry speed and examine the physical feasibility of such a feat. Join us for an educational journey