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Suppose you use videos to analyze the motion of penguinsas they slide from rest down three different frictionless ramps$(\mathrm{A}, \mathrm{B}, \mathrm{C})$ and into the water. The distances they travel and thetimes elapsed are recorded in the following table:(a) Find the magnitude of the penguin's acceleration for eachramp. Assume the acceleration is uniform. (b) Determine theinclination angle $\theta$ above horizontal for each ramp, assuming thatthe accelerations for part (a) are in close agreement with the formula, $a=g \sin \theta .$ (We will derive this formula in Chapter 5.)

(a)(i) Ramp $A : a=1.7 \mathrm{m} / \mathrm{s}^{2}$(ii) Ramp $\mathrm{B} : a=3.36 \mathrm{m} / \mathrm{s}^{2}$(iii) Ramp $\mathrm{C} : a=4.91 \mathrm{m} / \mathrm{s}^{2}$(b)(i) Ramp $A : \theta=9.98^{\circ}$(ii) Ramp $B : \theta=20.03^{\circ}$(iii) Ramp $C : \theta=30.03^{\circ}$

Physics 101 Mechanics

Chapter 2

One-Dimensional Kinematics

Motion Along a Straight Line

Cornell University

Rutgers, The State University of New Jersey

University of Washington

Hope College

Lectures

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In mathematics, algebra is…

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ssm A penguin slides at a …

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Figure $5-49$ shows four p…

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The masses $m_{\mathrm{A}}…

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Show that the acceleration…

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The tilt angle $\theta$ th…

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A loaded penguin sled weig…

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So in this problem, we have measurements off Penguins is lighting down from treat different rents into the water. So that's written here. The distance and the time Off each ramp we have four point 09 through 0.19 for the ramp A. We have one points and 96 and let's see, one wants you to wait for rank B and for upsy we have won 20 right and zero point 66 tree. Okay, so first of all, the problem wants us to discover the magnitude of the acceleration in each room. And how are we going to describe this? We know this is emotion with acceleration, so we can use do secretion. Here is the position as a function of time to describe the position of the of the penguins. So the initial position is here. The initial velocity is also zero. So we're going to have X equals GT. That's called actually a because it's not gravity. Acceleration is just on acceleration. A. The square divided by two. Okay, so for their ramp A, we have acceleration off. Let's see, 4.9 times two divided by 2.19 you square. This is it close to one point seven meters per second square. This is the acceleration off the ramp. A Let's do the same to the others in order Page. Did your room be We're going to have, do you? Acceleration. It grows two nights. See? 1.96 times two divided by 1.8 the square. Okay, so that's calculate this. This is it crawls through three point 36 meters her second square and the final ramp. We have acceleration off 1.0 rates times two divided by general 0.663 your 0.66 three square and the final acceleration is going to be four point nine one. You just your second square. Okay. The second item of the problem, uh, problems say's that our acceleration is described us g sign of Tita. And we need to discover Tita angle for each one of the accelerations we believe it previously discover. So I just need to do the first deceleration is 1.7. So we going to do for Darren? Hey, going to be 1.7 equals nine point 81. Sign off teeter So sign of Tito. It's going to be one 0.7, divided by 9.81. This is a close to let's see 0.17 17 tree and the value off teeter. Using a calculator, we can discover that he's it's nine. Going nine eight, the grease during They're saying 20 other too accelerations. We're going to have three point 36 it close. Nine point 81. Sign of teacher So sign of teacher secret three point 36 Divided by knifepoint 81. This is 3.36 divided by nine point anyone. Zero point tree for two in the value off Teeter. With this second room, it's going to be 20 0.0. Tree the grease and the last one for the third rent. The ramp, See is just 4.91 equals nine point 81. Seen sign off Peter. So sign of Tita is four point. Anyone divided by nine points and you're one. This is going to be 0.5. So Tito So Tito is just 30 point zero tree Greece. And that's the final answer to the question

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