The coordinates of a bird flying in the xy-plane are given by x(t)=t and y(t)=3.
ID: 1594090 • Letter: T
Question
The coordinates of a bird flying in the xy-plane are given by x(t)=t and y(t)=3.0mt2, where =2.4m/s and =1.2m/s2 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 3t and the y component is 4t, then you should enter 3t,4t. Express your answer using two significant figures for all coefficients. 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 3t and the y component is 4t, then you should enter 3t,4t. Express your answer using two significant figures for all coefficients. Part C Calculate the magnitude of the bird's velocity at t=2.0s. Express your answer using two significant figures. Part D Let the direction be the angle, that the vector makes with the +x-axis measured counterclockwise. Calculate the direction of the bird's velocity at t=2.0s. Express your answer in degrees using two significant figures. Part E Calculate the magnitude of the bird's acceleration at t=2.0s. Express your answer using two significant figures. Part F Calculate the direction of the bird's acceleration at t=2.0s. Part G At t=2.0s, is the bird speeding up, slowing down or moving at constant speed? At , is the bird speeding up, slowing down or moving at constant speed? speeding up slowing down moving at constant speed
Explanation / Answer
(A). (vx,vy) = (dx/dt, dy/dt) = (, -2t) =(2.4,-2.4t)
(B). (ax,ay)= (dvx/dt, dvy/dt) =(0, -2) = (0 , -2.4)
(C). v= sqrt(vx^2 + vy^2) = sqrt( 3.0^2 + (-4.8)^2) = 5.66 m/s
(D). tan(angle) = vy/vx = -4.8/3.0
=> angle= arctan(-1.6)= -58 degrees
(E). a = sqrt(ax^2 + ay^2) = 2.4
(F). Negative y-direction at all times
= theta = (270) degrees
(G). Constant acceleration in the y direction speeds up the bird.
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