Physics, 02.07.2019 13:40 nyed5789

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 +14 m/s and measures a time of 17.8 s before the rock returns to his hand. what is the acceleration (magnitude and direction) due to gravity on this planet? (indicate direction by the sign of the acceleration.)

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local acceleration due to gravity is -1.6 m/s The rock will have a constant deceleration due to the force of gravity and will travel for half the time until it reaches its peak altitude and then fall for the remaining time until it impacts the astronaut's hand. So first calculate how long it takes for the rock to reach its peak altitude by dividing the total time by 2. 17.8 s / 2 = 8.9 s Now the rock's velocity changes from +14 m/s to 0 m/s over a time period of 8.9 s. That gives us the following equation 14 m/s + 8.9x s = 0 Solve for x by first subtracting 14 m/s from both sides 8.9x s = -14 m/s Now divide both sides by 8.9 s x = -1.573 m/s^2 Since we only have 2 significant digits, round the result to 2 significant digits. x = -1.6 m/s

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russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

$x(t)=ax(x-6)$

where $a$ is unknown. because the position is parabolic, there is symmetry about the midpoint at $t=3$ , and we know that

$x(3)=10\implies -9a=10\implies a=-\dfrac{10}9$

so that the position function is

$x(t)=-\dfrac{10}9x(x-6)$

which means the velocity is

$v(t)=\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{20}9x+\dfrac{60}9$

then the total distance traveled is

$\displaystyle\int_{t=0}^{t=6}|v(t)|\,\mathrm dt=\left\{\int_{t-0}^{t=3}-\int_{t=3}^{t=6}\right\}v(t)\,\mathrm dt=20$

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at $x=0$ and ends at $x=0$ , so its displacement is 0.

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An astronaut on a distant planet wants to determine its acceleration due to gravity. the astronaut t...

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