Instantaneous Acceleration in 2D Video Lessons

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Problem: Using a reference frame with the origin at the take-off airport, the positive x-axis due East, and the positive y-axis due North, the acceleration a of an airplane as a function of time can be described as: a = (αt)î + (βt 4 − γt)ĵ, with α, β, and γ positive and constant. Assuming that the airplane takes off from the airport at time t = 0 with zero initial velocity: a) What are the units of α, β, and γ? b) Find the time(s) when the airplane position is directly NE of the airport. c) Find the trajectory of the plane, y(x). Write your results in terms of α, β, and γ. Remember to check the dimensions/units for each answer.

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Problem Details

Using a reference frame with the origin at the take-off airport, the positive x-axis due East, and the positive y-axis due North, the acceleration a of an airplane as a function of time can be described as:

a = (αt)î + (βt 4 − γt)ĵ,

with α, β, and γ positive and constant.

Assuming that the airplane takes off from the airport at time t = 0 with zero initial velocity:

a) What are the units of α, β, and γ?

b) Find the time(s) when the airplane position is directly NE of the airport.

c) Find the trajectory of the plane, y(x).

Write your results in terms of α, β, and γ. Remember to check the dimensions/units for each answer.

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Instantaneous Acceleration in 2D concept. You can view video lessons to learn Instantaneous Acceleration in 2D. Or if you need more Instantaneous Acceleration in 2D practice, you can also practice Instantaneous Acceleration in 2D practice problems.

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Based on our data, we think this problem is relevant for Professor Costanza's class at USF.