Calculate Position & Acceleration Vectors of Bird in xy-Plane

  • Thread starter Xtasy
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In summary, the bird's position vector is given by r(t) = ((a-bt^2),(ct^2)/2) where a, b, and c are constants representing the velocity of the bird. The acceleration vector is given by (0, -2ct) and the bird's altitude as it passes over x=0 after t=0 can be found by plugging in t=1 into the y-component of the position vector.
  • #1
Xtasy
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A bird flies in the xy-plane with a velocity vector given by v(vector) = (a-bt^2)(i-vector) + ct (j-vector) , with a= 2.4m/s, b=1.6m/s^3,c=4.0m/s^2. The positive y-direction is vertically upward. At t=0 the bird is at the origin.

Calculate the position vector of the bird as a function of time.
Express your answer in terms of a, b, and z. Write the vector r(t) in the form vector(r(t)x,r(t)y , , where the x and y components are separated by a comma.

Calculate the acceleration vector of the bird as a function of time. also in the form as stated above.

What is the bird's altitude (y-coordinate) as it flies over x=0 for the first time after t=0?
 
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  • #2
I see, good standard questions... :rolleyes:

Let's see how you are tackling them!
 
  • #3
Well, atiderviative will give me the position vector, but I don't know if I should plug in the values of a, b, etc. prior to me taking the antiderivative. Also I am not sure what form they are talking about.

For the acceleration the derivative is needed.

Not sure about the last question
 
  • #4
a, b, c are constants.

For the last question look at the position function, what can you notice?
 
  • #5
I notice that x=0, so there is no horizontal motion. What do they mean by birds altitude as it flies over x=0 after t=0, meaning whent t=1. Also so since x=0 I only focus on the y componet of the position vector, which is (ct^2)/2?
 
  • #6
Look at the acceleration vectorial function, it's x component is negative, so sooner or later the bird will pass the straight line x=0.
 

Related to Calculate Position & Acceleration Vectors of Bird in xy-Plane

1. How do you calculate the position vector of a bird in the xy-plane?

The position vector of a bird in the xy-plane can be calculated by using the bird's starting position, velocity, and time. You can use the formula r = r0 + vt where r is the position vector, r0 is the starting position, v is the velocity, and t is the time. This will give you the bird's position at a specific point in time.

2. How do you calculate the acceleration vector of a bird in the xy-plane?

The acceleration vector of a bird in the xy-plane can be calculated by using the bird's starting velocity, final velocity, and time. You can use the formula a = (v - v0) / t where a is the acceleration vector, v is the final velocity, v0 is the starting velocity, and t is the time. This will give you the bird's acceleration at a specific point in time.

3. What is the difference between position vector and acceleration vector?

The position vector and acceleration vector are both vectors that describe the motion of an object. The position vector describes the location of an object at a specific point in time, while the acceleration vector describes the rate at which an object's velocity is changing. In other words, the position vector tells you where the object is, while the acceleration vector tells you how the object is moving.

4. How do you represent a bird's motion in the xy-plane?

A bird's motion in the xy-plane can be represented by a graph, with the x-axis representing time and the y-axis representing the bird's position or velocity. This graph can show the bird's position, velocity, and acceleration at different points in time, allowing you to visualize its motion.

5. What factors can affect a bird's position and acceleration in the xy-plane?

The position and acceleration of a bird in the xy-plane can be affected by various factors, such as wind speed and direction, air resistance, and the bird's own physical abilities. Other factors, such as obstacles in the bird's path or changes in its surroundings, can also affect its motion in the xy-plane. Additionally, the bird's own movements and behavior, such as flapping its wings or changing direction, can also impact its position and acceleration in the xy-plane.

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