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Ok I'm havin troubles trying to solve this calculus problem.

-Rolling a Ball Bearing-

A ball bearing is placed on an incline plane and begins to roll. The angle of elevation of the plane is θ.

The distance (in meters) the ball bearing rolls in t seconds is

s(t) = 4.9(sin θ)t^2

a. Determine the speed of the ball bearing.

b. What value of θ will produce the maximum speed at a particular time.

Ok so here is how I "tackled" the problem.

ok part a, asks for speed so I take the derivative of the function to get velocity.

v(t) = (0)(sin θ)(t^2) + (4.9)(cos θ)(t^2) + (4.9)(sin θ)(2t)

v(t) = 4.9(t^2)(cos θ) + (9.8t)(sin θ)

ok now from here I'm not sure if my next steps are right...

Ok since they asked for the speed, i'm assuming they want an actual value....versus what I have thus far....

ok now setting what I have for v(t) to zero, I solve for t,

thus I get: t = -2tan θ

Now I take that value and put it back in to my original equation.

Now I have s(t) = 4.9(sin θ)(-2tan θ)^2

Now I solve for θ, by setting s(t) equal to zero.

but I end up with this....

4 = (cos θ)^2, and I don't think this is the right answer...

So any help on this would be nice,

Thanks.

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# Hard Calculus Word Problem

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