The coordinates of a bird flying in the xy-plane are given by x(t) = alphat and

Question

The coordinates of a bird flying in the xy-plane are given by x(t) = alphat and y(t) = 3. 0m - betat2 - where alpha = 2. 4 m/s and beta = 1. 2 m/s2. 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 3t and the y component is 4t, then you should enter 3t, 4t. Express your answer using two significant figures for all coefficients. 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 3t and the y component is 4t, then you should enter 3t, 4t. Express your answer using two significant figures for all coefficients. Calculate the magnitude of the bird's velocity at t = 2. 0s. Express your answer using two significant figures. Let the direction be the angle that the vector makes with the +x-axis measured counter clockwise Calculate the direction of the bird's velocity at t = 2. 0s. Express your answer in degrees using two significant figures. Calculate the magnitude of the bird's acceleration at t = 2. 0s. Express your answer using two significant figures. Calculate the direction of the bird's acceleration at t = 2. 0s.

Explanation / Answer

x(t)=a t
y(t)=bt^2

then the position vector, r, is given by

r= at i + bt^2 j where i and j are unit vectors in the x, y directions

velocity is then

v = dr/ dt = a i+ 2 b tj

a= dv/dt = 2b j

at t=2, v = a i + 4b j
speed = sqrt[a^2+16b^2]

direction of velocity is given by tan(theta)=4b/a

acceleration is constant with magnitude 2b in the j direction

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