Physics, 05.07.2019 04:00 lkhushi

In explaining this. dont understand at all

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Answer from: rprest00

For the first minute, the rocket is traveling straight upward at a constant velocity of 600 m/s. This means that after 1 minute (60 seconds), it will have risen to an altitude of

$y=\left(600\,\dfrac{\rm m}{\rm s}\right)(60\,\mathrm s)=36000\,\mathrm m$

From this point on, it's in freefall with a starting height of 36000 m, a starting velocity of 600 m/s upward, and accelerating downward with a magnitude of 1g. At its maximum height, the rocket's velocity will be 0. We have a formula that ties all this information together:

$-\left(600\,\dfrac{\rm m}{\rm s}\right)^2=2(-g)(y_{\rm max}-36000\,\mathrm m)$

$\implies y_{\rm max}=54367\,\mathrm m\approx54000\,\mathrm m$

(rounding to 2 significant digits)

The altitude of the rocket with respect to time (AFTER the first minute) is given by

$y=36000\,\mathrm m+\left(600\,\dfrac{\rm m}{\rm s}\right)t-\dfrac g2t^2$

The time it takes for the rocket to reach the ground ( y=0 ) is given by

$0=36000\,\mathrm m+\left(600\,\dfrac{\rm m}{\rm s}\right)t-\dfrac g2t^2$

$\implies t=166.56\,\mathrm s$

which means the rocket will have spent a TOTAL time of 226.56 seconds, or approximately 230 seconds, in the air.

Answer from: Quest

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.

Answer from: Quest

The geological theory that states that pieces of earth's lithosphere are in constant slow motion is the theory of plate tectonics.

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