Physics, 17.08.2020 05:01, LukeneedhelpInMath

A body of mass 0.5kg is shot vertically into the air with an initial speed of 45m/s , calculate the time taken to reach the maximum height

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answered: aidenbender06

The time to reach the maximum height is approximately 4.59 seconds

Explanation:

The maximum height in a problem where friction with the air is neglected, only needs the kinematic information of the initial velocity at which the object was launched vertically.

Recall that the formula for the velocity of an object under constant acceleration () in terms of time (t) is given by:

$v(t)=v_0+a\,\,t$

where v_0 is the initial velocity of the object (in our case the speed at which it was launched up in the air = 45 m/s)

Considering that the acceleration the object is subjected (which is the acceleration of gravity g = 9.8 m/s^2) is acting in opposite direction to the initial velocity of the object, we make sure to include a negative sign in the formula:

$v(t)=v_0+a\,\,t=v_0-g\,\,t$

then, considering that at the time the object reaches its maximum height, is when it stops and starts it motion back towards earth, that is the point at which the object's velocity is zero. Then we can solve for the time as follos:

$0=v_0-g\,\,t\\g\,\,t=v_0\\t=\frac{v_0}{g} \\t=\frac{45}{9.8} \\t\approx 4.59\,\,sec$

answered: Guest

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.

answered: Guest

Answer it orbits high above earth to gain clearer images of light, it magnifies images relative to the human eye, it records most of the universe as it was in the past, not as it is now;

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A body of mass 0.5kg is shot vertically into the air with an initial speed of 45m/s , calculate the...