Ch 03: Motion in Two or Three Dimensions
Chapter 3, Problem 3
The coordinates of a bird flying in the xy-plane are given by x(t) = αt and y(t) = 3.0 m − βt2, where α = 2.4 m/s and β = 1.2 m/s2. (c) Calculate the magnitude and direction of the bird's velocity and acceleration at t = 2.0 s.
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Textbook Question
A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft to the blade tip. The model is rotated in a wind tunnel at 550 rev/min. (a) What is the linear speed of the blade tip, in m/s?
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Textbook Question
A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft to the blade tip. The model is rotated in a wind tunnel at 550 rev/min. (b) What is the radial acceleration of the blade tip expressed as a multiple of g?
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Textbook Question
At its Ames Research Center, NASA uses its large '20-G' centrifuge to test the effects of very large accelerations ('hypergravity') on test pilots and astronauts. In this device, an arm 8.84 m long rotates about one end in a horizontal plane, and an astronaut is strapped in at the other end. Suppose that he is aligned along the centrifuge's arm with his head at the outermost end. The maximum sustained acceleration to which humans are subjected in this device is typically 12.5g. (a) How fast must the astronaut's head be moving to experience this maximum acceleration?
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Textbook Question
A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by v = [5.00 m/s − (0.0180 m/s3)t2]î + [2.00 m/s + (0.550 m/s2)t]ĵ. (b) What are the magnitude and direction of the car's velocity at t = 8.00 s? (b) What are the magnitude and direction of the car's acceleration at t = 8.00 s?
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Textbook Question
A 124-kg balloon carrying a 22-kg basket is descending with a constant downward velocity of 20.0 m/s. A 1.0-kg stone is thrown from the basket with an initial velocity of 15.0 m/s perpendicular to the path of the descending balloon, as measured relative to a person at rest in the basket. That person sees the stone hit the ground 5.00 s after it was thrown. Assume that the balloon continues its downward descent with the same constant speed of 20.0 m/s. (a) How high is the balloon when the rock is thrown?
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Textbook Question
A 124-kg balloon carrying a 22-kg basket is descending with a constant downward velocity of 20.0 m/s. A 1.0-kg stone is thrown from the basket with an initial velocity of 15.0 m/s perpendicular to the path of the descending balloon, as measured relative to a person at rest in the basket. That person sees the stone hit the ground 5.00 s after it was thrown. Assume that the balloon continues its downward descent with the same constant speed of 20.0 m/s. (c) At the instant the rock hits the ground, how far is it from the basket?
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