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

A particle is moving down a spiral path parameterized by: x = cos(au), y = sin(au), z = -u, where 0 \leq u \leq b (a,b real, >0). Starting from rest, the particle moves down the spiral under the influence of gravity and free from friction. Let g be the positive gravitational constant (so we're not assuming any value for g or particular units)

Find the position vector as a function of time.

Find the time it takes the particle to travel from the top of the spiral to the bottom.

Find the distance traveled by the particle.

Find the velocity of the particle when it reaches the bottom.

2. Relevant equations

3. The attempt at a solution

Initially, I used the vector < 0, 0, -g > for the acceleration, then integrated w/ respect to t (twice) to obtain expressions for the velocity and position in terms of t... then plugged in the expression (1/2)gt^2 for u in the parameterization to get the position vector of the particle. I feel pretty confident that this isn't correct.

I think I need to make use of the tangential acceleration, but I'm not entirely sure what to do. I think this problem is eating my brain, and would greatly appreciate any help :)

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# Homework Help: Cal 3 problem that is eating my brain - particle along a spiral path

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