Physics, 15.11.2019 01:31 janahiac09

In a pool game, the cue ball, which has an initial speed of 2 m/s, makes an elastic collision with the eight ball, which is initially at rest. the two balls have equal masses of 6 kg. after the collision, the eight ball moves at an an angle of 50.7 ◦ to the original direction of the cue ball.

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Answer from: jaccamoboy

The direction of motion of the cue ball is 39.3°.

Explanation:

Given that,

Initial speed = 2 m/s

Two balls have equal masses = 6 kg

After the collision,

The eight ball moves at an angle of 50.7° to the original direction of the cue ball.

Suppose we need to calculate the direction of motion of the cue ball after the collision

We need to calculate the direction of motion of the cue ball

If the collision is elastic,

Using conservation of energy

$\dfrac{1}{2}m_{A}v_{iA}^2+\dfrac{1}{2}m_{B}v_{iB}^2=\dfrac{1}{2}m_{A}v_{fA}^2+\dfrac{1}{2}m_{B}v_{fB}^2$

Where, $m_{A}$ = mass of the cue ball

$m_{B}$ = mass of the eight ball

The two balls have equal masses.

So $m_{A}=m_{B}$

$v_{iA}^2+0=v_{fA}^2+v_{fB}^2$

The angle of the cue ball after the collision

$\theta_{A}+\theta_{B}=90^{\circ}$

$\theta_{A}=90-\theta_{B}$

Put the value into the formula

$\theta_{A}=90-50.7$

$\theta_{A}=39.3^{\circ}$

Hence, The direction of motion of the cue ball is 39.3°.

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

Which of the following are risk factors for emphysema ? correct answer : a and and c good luck and have a nice benevolentpuppy day! : )

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In a pool game, the cue ball, which has an initial speed of 2 m/s, makes an elastic collision with t...