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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
- WhomeLv 77 years agoFavorite 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.