Explanation Given data: A trampolinist flies straight up into the air, and then back down onto the trampoline, where she comes instantaneously to rest when the trampoline is fully stretched. From the given data, the following are the three various positions of the trampolinist in her ride. a. When she is instantaneously at rest. b. Just before she leaves the trampoline. c. When she is at the top of her flight. Formula used: Write the expression for apparent weight of the trampolinist when she moves in the upward direction as follows. w app = w + m a y (1) Here, w is the weight of the trampolinist when she is in equilibrium state, m is the mass of the trampolinist, and a y is the acceleration of the trampolinist in the upward direction. Write the expression for apparent weight of the trampolinist when she moves in the downward direction as follows. w app = w − m a y (2) Here, ( − a y ) is the acceleration of the trampolinist in the downward direction. Write the expression for the weight of the trampolinist as follows. w = m g (3) Here, g is the acceleration due to gravity of the earth, which is 9.8 m s 2 . Write the expression for acceleration of the trampolinist by using the kinematic equation as follows. a y = ( v y ) f − ( v y ) i Δ t (4) Here, ( v y ) i is the initial speed of the trampolinist, ( v y ) f is the final speed of the trampolinist, and Δ t is the change in the time. Explanation: Analyze the apparent weight of the trampolinist for the given positions as follows. a. When she is instantaneously at rest: The trampolinist starts from the surface of the trampoline, then moves in the upward direction, and then she falls from the highest flight to the fully stretched position of the trampoline. The trampolinist is instantaneously at rest where the trampoline is fully stretched. The expression in equation (2) is applicable for the apparent weight at the given position. The trampolinist has zero final velocity, but she accelerates downward direction. Substitute 0 m s for ( v y ) f in equation (4), a y = 0 m s − ( v y ) i Δ t = − ( v y ) i Δ t Substitute [ − ( v y ) i Δ t ] for a y in equation (2), w app = w − m [ − ( v y ) i Δ t ] w app = w + m ( v y ) i Δ t (5) Therefore, the apparent weight of the trampolinist at the given position is [ w + m ( v y ) i Δ t ]

4th Edition

ISBN: 9780134700427

Author: Knight

Publisher: PEARSON

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Chapter 5, Problem 13CQ

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Chapter 5, Problem 12CQ

Chapter 5, Problem 14CQ

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