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Best_Mathematician
 2 years ago
calculus help...plz explain and answer question...i totally dont know what they are...studying on my own
Best_Mathematician
 2 years ago
calculus help...plz explain and answer question...i totally dont know what they are...studying on my own

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phi
 2 years ago
Best ResponseYou've already chosen the best response.1r is a position vector... the position of a point that changes with time. it has components in the x direction (the "ith" component) and y direction the velocity of the point is dr/dt (derivative with respect to time) you take the derivative of each component separately.... you get a new vector that represents the velocity in the x and y dimensions...

phi
 2 years ago
Best ResponseYou've already chosen the best response.1it is not obvious, but they mean v is the velocity vector and a is the acceleration vector (2nd derivative of r, and the 1st derivative of v)

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0(tsint)i = (1cost)i = (sint)i (1cost)j = (sint)j = (cost)j f(x) f'(x) f''(x)

phi
 2 years ago
Best ResponseYou've already chosen the best response.1r= (tsin t) i + (1cos t) j v= dr/dt = (1cos t) i + sin t j or v= < (1cos t, sin t> the magnitude of v is found by doing the dot product v^2 = v dot v and v = sqrt( v dot v)

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0what is dot product

phi
 2 years ago
Best ResponseYou've already chosen the best response.1Khan has videos on vectors. See http://www.khanacademy.org/math/linearalgebra/vectors_and_spaces/dot_cross_products/v/vectordotproductandvectorlength Here is one from the physics playlist http://www.khanacademy.org/science/physics/electricityandmagnetism/v/thedotproduct which might be better. But the dot product is the sum of the product of corresponding elements. In this case < (1cos t, sin t> dot < (1cos t, sin t> = (1cos t)^2 + (sin t)^2 which simplifies to v = 2(1 cos t)

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0ohk got it...so how to get minimum nd maximum values

phi
 2 years ago
Best ResponseYou've already chosen the best response.1we know cos t has a max of +1 and a min of 1, so v ranges between 2(11) and 2(1  (2)) or 0 and 4

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0plz carry on

phi
 2 years ago
Best ResponseYou've already chosen the best response.1a= < sin t , cos t> can you find its dot product (that gives you a^2 )

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0sin^2t+cos^2t = 1

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0am i on track?

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0ok so min and max for velocity is 0 and 4 repectively and min and max for acceleration is 1 and 1...correct?

phi
 2 years ago
Best ResponseYou've already chosen the best response.1the magnitude of the acceleration is always 1, but its direction is changing.

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0oh ya but we do not need to care about direction...right?

phi
 2 years ago
Best ResponseYou've already chosen the best response.1you might care if you were trying to analyze what is going on... but you don't need the direction if all you care about is the magnitude.

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0ok so how to do rest of the part

phi
 2 years ago
Best ResponseYou've already chosen the best response.1I am not sure what they want for a plot... for the smaller hoop, make the frequency twice as fast. that means in sin t and cos t replace t with 2t this will make the hoop spin twice as fast.

Best_Mathematician
 2 years ago
Best ResponseYou've already chosen the best response.0ok so what is the vector function that models the behavior
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