The coordi.nates of a bird flying in the xy-plane are given by X(I) = al and y(l

Question

The coordi.nates of a bird flying in the xy-plane are given by X(I) = al and y(l) = 3.0 m -{312, where a = 2.4 m/s and (3 = 1.2 m/ s2 (a) Sketch the path of the bird between I = 0 and I = 2.0 s. (b) Calculate the velocity and acceleration vectOIs of the bird as functions of time. (c) Calculate the magnitude and direction of the bird's velocity and acceleration at I = 2.0 s.
(d) Sketch the velocity and acceleration vectors at t = 2.0 s. At this instant. is the bird speeding up, is it slowing down. or is its speed instantaneously not changing') Is the bird turning? If so, in what direction?

Explanation / Answer

b)

x(t) = a t

y(t) = 3.0 - B t^2

vx = a = 2.4 m/s

vy = - 2 B t = -2*1.2 t = -2.4 t

v = (2.4 , -2.4 t) m/s

a = (o, -2.4) m/s2

c)

v = (2.4, -2.4*2) = (2.4, -4.8)

v = (2.4*2.4 + 4.8*4.8) = 5.4 m/s

= 360 - Arctan(4.8/2.4) = 297 degrees

d)

The bird is speeding up.

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