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Physics help, not sure why I'm getting it wrong?

A particle's position is given by : x(t) = (3t - 2t^2)x + (2 + sin(pi*t))y

Find the angle between the acceleration and position vectors at t = 0.5

First, I calculated the acceleration vector to be:

a(t) = -4x - (pi^2)sin(pi*t)y

With a double derivation, which holds up even under a derivation calculator

Then I plugged t=0.5 into both equations, and got

x(.5) = 1x + 2.03y

a(0.5) = -4x - 0.27y

So my vectors are [1, 2.03] and [-4, -0.27]

I can use either trigonometry or the dot product-length-angle relation, and no matter what, I end up with an angle of 120. This is different than the correct answer of 176 degrees, and I have no idea why. Can anyone help?

1 Answer

Relevance
  • Whome
    Lv 7
    7 years ago
    Favorite Answer

    I think you have a calculation error when you enter the 0.5 value into the position and accelerations equations

    set your calculator to radians

    I get

    x(0.5) = 1i + 3j

    a(0.5) = -4i - π²j

    I believe your answer will develop from there. Remember to convert back to degrees at the proper time.

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