(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A 0.39 kg particle moves in an xy plane according to x(t) = - 13 + 1 t - 6 t^3 and y(t) = 28 + 5 t - 11 t^2, with x and y in meters and t in seconds. At t = 1.0 s, what are (a) the magnitude and (b) the angle (within (-180°, 180°] interval relative to the positive direction of the x axis) of the net force on the particle, and (c) what is the angle of the particle's direction of travel?

2. Relevant equations

F(y) = ma(y)

F(x) = ma(x)

3. The attempt at a solution

Well I've got the magnitude of the force correct as 16.45N after finding the second derivative of x and y and then using Pythagoras's theorem.

What I'm struggling with is part B and C. From what I understand both answers should be the same, as the direction of Fnet should be the direction of travel.

I attempted to calculate the angle between the force and the y axis. I used sin^-1 theta = 22/28.43. This gave me a value for theta of 50.71 degrees. I then added 90 degrees to this to get the angle relative to the positive x axis. Getting an answer of 140.71 degrees for both B and C. But this is apparently wrong.

Where did I go wrong?

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# Particle of certain mass moving in an xy plane

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