Kinematics Question - Need Help Desperately

[Joe_K]

Homework Statement

An unsuspecting bird is coasting along in an easterly direction at 1.34 m/s when a strong wind from the south imparts a constant acceleration of 0.200 m/s^2. If the acceleration from the wind lasts for 3.90s, find the magnitude, r, the direction, theta, of the bird's displacement during this time period. (HINT: assume the bird is originally traveling in the +x direction)

Homework Equations

The Attempt at a Solution

I missed a day of class, and I am not really sure what the equations are that I am supposed to use for this type of question. Can anyone help me get going on this problem? Thanks in advance.

 

[gneill]

The problem is much like the usual projectile kind of problem. There's an initial velocity in the x-direction and an acceleration in the y-direction. The motions are independent. Compute both over the given time interval. Treat as vector components for the total displacement.

 

[Joe_K]

The problem is much like the usual projectile kind of problem. There's an initial velocity in the x-direction and an acceleration in the y-direction. The motions are independent. Compute both over the given time interval. Treat as vector components for the total displacement.

Thank you for your help, I am still a little confused as to what you mean by "compute over the given time interval"

 

[gneill]

Thank you for your help, I am still a little confused as to what you mean by "compute over the given time interval"

What's the x-direction displacement after the stated time? What's the y-direction displacement after the given time?

 

[rwisz]

I would suggest that you first start by defining the problem and identifying the known and unknown variables. In this case, the problem is asking for the magnitude and direction of the bird's displacement after experiencing a constant acceleration from the wind. The known variables are the initial velocity of the bird (1.34 m/s), the acceleration from the wind (0.200 m/s^2), and the time period (3.90s). The unknown variables are the magnitude (r) and direction (theta) of the bird's displacement.

Next, you can use the equations of kinematics to solve for the unknown variables. In this case, you can use the equation r = r0 + v0t + 1/2at^2, where r0 is the initial position, v0 is the initial velocity, a is the acceleration, and t is the time period. Since the bird is initially traveling in the +x direction, the initial position (r0) can be assumed to be 0.

Plugging in the known values, we get r = 0 + (1.34 m/s)(3.90s) + 1/2(0.200 m/s^2)(3.90s)^2 = 5.23 m. This is the magnitude of the bird's displacement.

To find the direction, we can use the equation theta = tan^-1(vy/vx), where vy is the final vertical velocity and vx is the final horizontal velocity. In this case, the bird is not experiencing any vertical acceleration, so vy remains 0. Therefore, the direction theta = tan^-1(0/1.34) = 0 degrees.

So, the bird's displacement is 5.23 m in the +x direction. I hope this helps you with your homework. It is important to understand the equations and how to use them to solve problems in kinematics. Good luck!