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.

Ch 03: Motion in Two or Three Dimensions

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 03: Motion in Two or Three Dimensions

Problema 7a

Capitolo 3, Problema 7a

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.

Guida verificata passo dopo passo

Identify the equations of motion for the bird: x(t) = αt and y(t) = 3.0 m − βt², where α = 2.4 m/s and β = 1.2 m/s².

Substitute the given values of α and β into the equations: x(t) = 2.4t and y(t) = 3.0 − 1.2t².

Determine the coordinates of the bird at specific time intervals between t = 0 and t = 2.0 s. For example, calculate x(0), y(0), x(1), y(1), x(2), and y(2).

Plot these coordinates on the xy-plane to visualize the path. Start by marking the points (x(0), y(0)), (x(1), y(1)), and (x(2), y(2)).

Connect the plotted points with a smooth curve to represent the bird's path, noting that the x-coordinate increases linearly while the y-coordinate follows a parabolic trajectory.

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Parametric Equations

Parametric equations express the coordinates of points on a curve as functions of a parameter, often time (t). In this problem, x(t) = αt and y(t) = 3.0 m − βt² describe the bird's position in the xy-plane over time. Understanding these equations helps in plotting the trajectory by calculating x and y for various t values.

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Percorso guidato

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Kinematics Equations

Kinematics in Two Dimensions

Kinematics in two dimensions involves analyzing motion along two axes, typically x and y. The bird's motion is described by its horizontal and vertical components, x(t) and y(t). This concept is crucial for understanding how the bird's position changes over time and how to sketch its path accurately.

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Percorso guidato

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Kinematics in 2D

Graphical Representation of Motion

Graphical representation involves plotting the path of an object based on its position equations. By calculating the bird's x and y coordinates at different time intervals, one can sketch its trajectory on the xy-plane. This visual representation helps in understanding the overall motion pattern and direction of the bird.

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Subtracting Vectors Graphically

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