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Solved: CALC The coordinates of a bird flying in the
Chapter 3, Problem 7E(choose chapter or problem)
Problem 7E
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?
Questions & Answers
QUESTION:
Problem 7E
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?
ANSWER:
Solution 7E
Step 1:
Provided, x(t) = 𝝰t
y(t) = 3.0 m - 𝝱t2
𝝰 = 2.4 m/s and 𝝱 = 1.2 m/s2
Put t = 0 s, then,
x(0) = 2.4 m/s × 0 s = 0 m
y(0) = 3.0m - (1.2 m/s2 × 0 s2) = 3.0m
Put, t = 1 s, then,
x(1) = 2.4 m/s × 1 s = 2.4 m
y(1) = 3.0m - (1.2 m/s2 × 1 s2) = 1.8 m
Put, t = 2 s, then,
x(2) = 2.4 m/s × 2 s = 4.8 m
y(1) = 3.0m - (1.2 m/s2 × 4 s2) = - 1.8 m
a) We can plot the graph as mentioned below in figure 1. The vertical axis represents y (t) and the horizontal axis represents x(t).
Figure 1