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

Question

The coordinates of a bird flying in the xy plane are given by x(t)=?t and y(t)=3.0m??t2, 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=2.0 s.

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=2.0 s.

Express your answer in degrees using two significant figures.

Part E)

Calculate the magnitude of the bird's acceleration at t=2.0 s.

Express your answer using two significant figures.

Part F) Calculate the direction of the bird's acceleration at t=2.0 s.

Explanation / Answer

A. (vx,vy) = (dx/dt, dy/dt) = (?, -2?t) =(3.0,-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) = 5.7 m/s
D. tan(angle) = vy/vx = -4.8/3.0 => angle= arctan(-1.6)= -58 degrees

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