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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?
Okay, thank you, I understand what's going on. My only question would be why I had to switch to radians. The answer I'm looking for is in DEGREES, so why do I have to work in radians and back again?
2 Answers
- az_lenderLv 77 years ago
x(0.5) = 1x + 3y
a(0.5) = -4x - 9.870y
What was going wrong for you was that your calculator was giving you the sine of (pi/2) DEGREES (like, 1.57 degrees), rather than the sine of pi/2 radians.
OK, then the dot product idea is the right one.
The dot product is -4 - 29.61 = -33.61.
The magnitude of x(0.5) is sqrt(10).
The magnitude of a(0.5) is 10.649
The angle is arccos [-33.61/(10.649*sqrt(10))]
= arccos (-0.99803) = 176.4 degrees.
