The coordinates of a bird flying in the xy-plane are given by [tex]x(t) = \alpha t[/tex] and [tex]y(t) = 3.0 \, \text{m} - \beta t^2[/tex], where [tex]\alpha = 2.4 \, \text{m/s}[/tex] and [tex]\beta = 1.2 \, \text{m/s}^2[/tex].
Part a: Calculate the velocity vector of the bird as a function of time. Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4.
Part b: Calculate the acceleration vector of the bird as a function of time. Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4.
Answer (2)
α = 2.4 s m
β = 1.2 s 2 m
x ( t ) = a t
y ( t ) = 3 − β t 2
V x ( t ) = α
V y ( t ) = − 2 β t
v ec t or V = [ α ; − 2 β t ]
a x ( t ) = 0
a y ( t ) = − 2 β t
v ec t or a [ 0 ; − 2 β t ]
The velocity vector of the bird as a function of time is (2.4, -2.4t). The acceleration vector is (0, -2.4). This means the bird is moving with a constant velocity in the x-direction and accelerating downward in the y-direction.
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