A bird flies in the xy-plane with a velocity vector givenby v = (α-βt2)i + γtj with α=2.4m/s,β=1.6m/s3 and γ=4m/s2 . Thepositive y-direction is vertically upward. At t=0 the birdis at the origin.

1. Calculate the position vector of the bird as a function oftime.
2. Calculate the acceleration vector of the bird as a function oftime.
3. What is the bird's altitude (y-coordinate) as it fliesover x=0 for the first time after t=0.

1.

2.

3.

Explanation:

The velocity vector is

1. The position vector can be found by integrating the velocity vector.

At t = 0, the bird is at the origin, so the integration constants can be determined.

Therefore, C1 and C2 are equal to zero.

2. The acceleration vector is the derivative of the velocity vector with respect to time.

3. We will first find the time when the x-component of the position vector is equal to zero.

We will plug in this value into the y-component of the position vector.

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