Question

1. The position of a bird in the xy-plane is given by ?⃗ = (3.0?−∝ ?)?̂+ ?? 2 ?̂where ∝= 1.6 ?/? and ? = 0.8 ?/? 2 . a) What are Vx(t) and Vy(t), x and y components of the velocity of the bird as a function of time? b) What is the bird’s net velocity at 3.0 s (magnitude and direction)? c) What are ax(t) and ay(t), x and y components of the acceleration of the bird as a function of time? d) What is the bird’s net acceleration at 3.0 s (magnitude and direction)? e) Sketch the velocity and acceleration vectors at 3.0 s. At this instant, is the bird speeding up, slowing down or is its speed instantaneously not changing? Is the bird turning? If so, in which direction? Explain your reasons.

Answer #1

Problem 3.12
Each of the following vectors is given in terms of its x- and
y-components.
Part A vx = 16 m/s , vy = 31 m/s . Find the vector's
magnitude.
Part B vx = 16 m/s , vy = 31 m/s . Find the vector's
direction.
Part C ax = 20 m/s2 , ay = 10 m/s2 . Find the vector's
magnitude.
Part D ax = 20 m/s2 , ay = 10m /s2 . Find the vector's
direction

The position of a bird flying parallel to the ground is given by
the following equation as a function of time:
?⃗ = [2.9? + (0.09 ?⁄?^2)?^2]?̂ − (0.015 ?⁄?^3)?^3?̂
(a) At what value of t does the velocity vector of the bird make an
angle of 30o clockwise from the +x axis?
(b) At the time calculated in part (a) what are the magnitude and
direction of the bird’s acceleration vector?

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