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So in this video are given off tea and were
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asked to determine the door bone tangential components of the
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exploration vector. So our team, you simply t
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I have Moscow sine squared Teoh a sine squared.
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So our priority way We just have to find the
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derivative of each component with respect so derivative of tea
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with respect to use one the derivative of course I
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square to use the changeable is just too close I
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t time. So this is a derivative of the
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outside derivative would be inside the derivative close scientists just
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negative sign. So in total we get negative to
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co scientist. Citing plus the derivative of science were
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Teoh perspective. You have to use a chain room
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. So it's to sigh Inti, that's a derivative
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of the outside times. The derivative of sine of
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t is closely so to scientific on 70 K Now
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we can use our trick identities so we know that
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well to sign beta co sign the lease just signed
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to theater So then these were going to get one
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. I have minus sign to t j have plus
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sign to Kiev I know are now the second derivative
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of our majestic, the derivative of our prime to
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teach. They're a bit of a former with respected
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t zero that inevitable negative cited. You respected t
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again. Train role begin Negative too. Uh,
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negative to sco sign t j a happ plus again
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they're gonna sign to feel respected. T general,
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We used to be willing to a close eye.
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Inti Chaos. Okay, so now we want to
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determine the magnitude of our privacy. Sort of take
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each component, square it and add it to bath
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. Together they take the square root. So swear
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Rose the square. So what was once we're plus
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signs where two teeth puts ice cream, I would
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take the square root of that. So that's just
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one plus two sides square two teeth. Okay.
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No. A sub t The tangential component of the
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explorations. Your spot prime of t dot r double
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o. T divided by our problems. So basically
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, what we're gonna do is we're gonna take each
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component and multiply it with each other. So one
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times 00 negative Sign, uh, to tee times
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Negative to co sign t will be positive to sign
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. T uh co signed 30 from Sai Inti and
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then, uh, that could multiply The cake combines
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together we get to sign to ti Ko sai.
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All right, so this is when we get right
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over here. So this is good zero. And
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then we have to sign to become some 20 plus
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to sign to t close I. And what we
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can do right now is that we can add the's
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together, so we're just gonna get So we add
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these two together, we just get for sign to
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t coastline, and that's pretty much it. So
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four signed. Two teeth close identity divided by the
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square root of one plus two have Science Square.
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All right now to determine that the normal component of
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the acceleration. First we determined the cross product.
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So have I. Had they had happened? We
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write our each component are far prime of being art
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double private t. So we get one negative scientist
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et sign to t zero negative to co sign into
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T two course on three teeth to return to find
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the I had component across these two. And then
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we find their determinant of once on the inside.
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This just negative scientific T times to close identity plus
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to co sign to t sign titty. So that's
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how we determine it. And then we realized that
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two components are the same. So this is simple
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zero now to find the jihad component across this across
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this point determining so one times to co sign to
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t buying his your attach signed to me, that's
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just too close. I duty. But since the
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jihad component, we have to foot the sign So
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it's negative to co sign to T. J.
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But the bill finally, where the key component across
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this across this we get across brother or we don't
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refine determinant. So it's one times negative Two cops
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trying to do is just negative two from sanctity buying
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a zero times negative scientist to you just get zero
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. So we have negative to t coastline. Do
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you have? So what survives are these? So
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we have zero. I have minus two coastline to
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t. J have my studio site T k A
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. And now, to determine the magnitude of what
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across product, we're gonna square each complaint and then
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take the square root of we have zero squared plus
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negative to co sign to t square loss. Negative
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to co sign to square which is just simply eight
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co sign square to t And now we take the
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square root of that So you can write that we
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can pull out a force are going to get to
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Times Square, vote off to t coastline square to
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t when we can, right two times the square
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root of two times the absolute value of coastline to
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because it's under the square roots which should always be
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positive. So that's where we put the absolute value
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, of course. All right now, Ace event
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is just the magnitude of our prime mufti cross with
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our double primal divides by the magnitude of our private
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T and we determined all the same to Times Square
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would have to I was the absolute by go side
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to t divided by one plus two sides square to
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t. And that is the normal component of the
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acceleration vector