CALC The coordinates of a bird flying in the xy -plane are given by x ( t ) = αt and y ( t ) = 3.0 m – βt 2 , where α = 2.4 m/s and β = 1.2 m/s 2 . (a) Sketch the path of the bird between t = 0 and t = 2.0 s. (b) Calculate the velocity and acceleration vectors of the bird as functions of time, (c) Calculate the magnitude and direction of the bird's velocity and acceleration at t = 2.0 s. (d) Sketch the velocity and acceleration vectors at t = 2.0 s. At this instant, is the bird’s speed increasing, decreasing, or not changing? Is the bird turning? If so, in what direction?
CALC The coordinates of a bird flying in the xy -plane are given by x ( t ) = αt and y ( t ) = 3.0 m – βt 2 , where α = 2.4 m/s and β = 1.2 m/s 2 . (a) Sketch the path of the bird between t = 0 and t = 2.0 s. (b) Calculate the velocity and acceleration vectors of the bird as functions of time, (c) Calculate the magnitude and direction of the bird's velocity and acceleration at t = 2.0 s. (d) Sketch the velocity and acceleration vectors at t = 2.0 s. At this instant, is the bird’s speed increasing, decreasing, or not changing? Is the bird turning? If so, in what direction?
CALC 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. (a) Sketch the path of the bird between t = 0 and t = 2.0 s. (b) Calculate the velocity and acceleration vectors of the bird as functions of time, (c) Calculate the magnitude and direction of the bird's velocity and acceleration at t = 2.0 s. (d) Sketch the velocity and acceleration vectors at t = 2.0 s. At this instant, is the bird’s speed increasing, decreasing, or not changing? Is the bird turning? If so, in what direction?
The position r→ of a particle moving in an xy plane is given by r→=(3.00t^3−7.00t)i^+(6.00−2.00t^4)j^ with r→ in meters and t in seconds. In unit-vector notation, calculate(a)r→, (b)v→, and (c)a→ for t = 2.00 s. (d) What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t = 2.00 s? Give your answer in the range of (-180o; 180o).
A particle moves in the xy plane, starting from the origin at t = 0 with an initial velocity having an x component of 20 m/s and a y component of 215 m/s. The particle experiences an acceleration in the x direction, given by ax =4.0 m/s2.(A) Determine the total velocity vector at any later time. (B) Calculate the velocity and speed of the particle at t = 5.0 s and the angle the velocity vector makes with the x axis. (C) Determine the x and y coordinates of the particle at any time t and its position vector at this time.
A rugby player runs with the ball directly toward his opponent’s goal, along the positive direction of an x axis. He can legally pass the ball to a teammate as long as the ball’s velocity relative to the field does not have a positive x component. Suppose the player runs at speed 4.0 m/s relative to the field while he passes the ball with velocity relative to himself. If has magnitude 6.0 m/s, what is the smallest angle it can have for the pass to be legal?
Chapter 3 Solutions
University Physics with Modern Physics (14th Edition)
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