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SSM A skateboarder, starting from rest, rolls down a 12.0-m ramp. When she arrives at the bottom of the ramp her speed is 7.70 m/s.(a) Determine the magnitude of her acceleration, assumed to be constant.(b) If the ramp is inclined at 25.0 with respect to the ground, what is the component of her acceleration that is parallel to the ground?

(a) $a=2.47 \mathrm{m} \cdot \mathrm{s}^{-2}$(b) $a_{x}=2.24 \mathrm{m} \cdot \mathrm{s}^{-2}$

Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

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04:16

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so the question states that a skater moves down a ramp that's 12 meters along and her initial speed is zero meters per second and her final speed is 7.7 meters per second and our goal is to find her acceleration. So to do this we can use the Kinnah Matic formula that states the the final velocity squared is equal to the initial boss D squared, plus two times the acceleration times, the change in displacement. So we know Delta X is equal to 12 meters. We also know that the initial velocity is equal to zero. And we think that I also know that the final velocity is equal to 7.7 meters per second. We complete that in into this formula appear and so for a. And when we do this, we see we get this equation where a is equal to 2.47 meters per second squared. The second part of the problem states that now the ramp is inclined at a 25 degree angle and we need to find the acceleration relative to the ground. So in this direction, we know that the acceleration that we got for the first part of the problem is down the ramp, so weaken Break up the components of this acceleration into a vertical component and a horizontal component. We know that this angle here is stada for 25 degrees, which is same thing as this angle here, this is data. So this angle here must be 90 minus data. And so if we want to find the component of acceleration here, which is relative to the ground, we need to take the acceleration A and multiply it by sign of 90 minus data. And the sign of 90 minus state is just the same thing as co sign of data. So if we take the acceleration from problem one and multiply it by co sign of 25 degrees, we should get our answer, which is 2.2 for meters per second squared.

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