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An astronaut on a distant planet wants to determine its acceleration due to gravity. The astronaut throws a rock straight up with a velocity of $+15 \mathrm{m} / \mathrm{s}$ and measures a time of 20.0 $\mathrm{s}$ before the rock returns to his hand. What is the acceleration (magnitude and direction) due to gravity on this planet?

$-1.5 m / s^{2}$

Physics 101 Mechanics

Chapter 2

Kinematics in One Dimension

Motion Along a Straight Line

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Washington

University of Sheffield

Lectures

04:16

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In mathematics, algebra is…

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On a planet far, far away,…

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in this problem. We have an astronaut that wakes up on a bizarre alien planet. Um, he's interested to figure out what the acceleration is on this planet. To see how close it is. Toothy earth, which is negative 9.8 meters per second squared. So he tosses an object straight up with a velocity of 15 meters per second. And this object hangs in the air much longer than it normally should and takes 20 seconds before it returns to his hand, meaning the displacement is going to be zero meters. Now, I'm looking for the acceleration here, which means I'm looking for my equation that has all three of those known values in it as well as a and doesn't have the final velocity in it. Which is gonna give me that last equation on my list that X equals V, not tea plus 1/2 a T squared. Okay, so when we plug our numbers in here, we get zero equals 300 close, 1/2 acceleration times 400. And when I rearrange us a little bit, we end up with zero equals 300 plus 200 times the acceleration, which gives me an acceleration of negative 1.5 meters per second squared for this bizarre alien planet

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