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Robophys
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Homework Statement
The position function of a projectile is given by r(t) = (5t + 6t2) m I + (30 - t3) m j. What is the displacement of the particle in magnitude angle form at the = 2.0 seconds.
Homework Equations
√x2+y2
tan-1 = y/x
Possibly: x = v0t + 1/2at2
The Attempt at a Solution
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I assumed you could calculate the position at t = 2.0 s by plugging into the position function and subtract the initial position. So the initial position would be 30 in the positive you direction (j) and 0 i. The position at t = 2.0 s would be 10 + 6 * 4 = 34 i and 30 - 8 = 22. So the displacement would then be 34 m in the positive x direction and 8 meters in the negative y directions The resultant magnitude would be √(34)2+(-8)2 = √1156 + 64 = √1220.
The angle would be tan-1θ = y over x then
Is this correct? I haven't encountered another problem finding displacement given position function. Or should I find initial velocity and acceleration and use x = v0t + 1/2at2.