Answer:
a) The x coordinate of the third mass is -1.562 meters.
b) The y coordinate of the third mass is -0.944 meters.
Explanation:
The center of mass of a system of particles (
), measured in meters, is defined by this weighted average:
(1)
Where:
- Mass of the i-th particle, measured in kilograms.
- Location of the i-th particle with respect to origin, measured in meters.
If we know that
,
,
,
,
and
, then the coordinates of the third particle are:
![(-0.500\,m, -0.700\,m) = \frac{(1\,kg)\cdot (-1.20\,m,0.500\,m)+(4.50\,kg)\cdot (0.600\,m,-0.750\,m)+(4\,kg)\cdot \vec r_{3}}{1\,kg+4.50\,kg+4\,kg}](https://tex.z-dn.net/?f=%28-0.500%5C%2Cm%2C%20-0.700%5C%2Cm%29%20%3D%20%5Cfrac%7B%281%5C%2Ckg%29%5Ccdot%20%28-1.20%5C%2Cm%2C0.500%5C%2Cm%29%2B%284.50%5C%2Ckg%29%5Ccdot%20%280.600%5C%2Cm%2C-0.750%5C%2Cm%29%2B%284%5C%2Ckg%29%5Ccdot%20%5Cvec%20r_%7B3%7D%7D%7B1%5C%2Ckg%2B4.50%5C%2Ckg%2B4%5C%2Ckg%7D)
![(-4.75\,kg\cdot m, -6.65\,kg\cdot m) = (-1.20\,kg\cdot m, 0.500\,kg\cdot m) + (2.7\,kg\cdot m, -3.375\,kg\cdot m) +(4\cdot x_{3},4\cdot y_{3})](https://tex.z-dn.net/?f=%28-4.75%5C%2Ckg%5Ccdot%20m%2C%20-6.65%5C%2Ckg%5Ccdot%20m%29%20%3D%20%28-1.20%5C%2Ckg%5Ccdot%20m%2C%200.500%5C%2Ckg%5Ccdot%20m%29%20%2B%20%282.7%5C%2Ckg%5Ccdot%20m%2C%20-3.375%5C%2Ckg%5Ccdot%20m%29%20%2B%284%5Ccdot%20x_%7B3%7D%2C4%5Ccdot%20y_%7B3%7D%29)
![(4\cdot x_{3}, 4\cdot y_{3}) = (-6.25\,kg\cdot m,-3.775\,kg\cdot m)](https://tex.z-dn.net/?f=%284%5Ccdot%20x_%7B3%7D%2C%204%5Ccdot%20y_%7B3%7D%29%20%3D%20%28-6.25%5C%2Ckg%5Ccdot%20m%2C-3.775%5C%2Ckg%5Ccdot%20m%29)
![(x_{3},y_{3}) = (-1.562\,m,-0.944\,m)](https://tex.z-dn.net/?f=%28x_%7B3%7D%2Cy_%7B3%7D%29%20%3D%20%28-1.562%5C%2Cm%2C-0.944%5C%2Cm%29)
a) The x coordinate of the third mass is -1.562 meters.
b) The y coordinate of the third mass is -0.944 meters.
Answer:
discrimination: prejudice towards a person/group based on their race, sex, age, and/or sexual orientation
Explanation:
People of color face discrimination because of the color of their skin.
Although scientists can't detect or observe black holes with telescopes that detect x-rays, light, or other many other different forms of electromagnetic radiation and waves. But they can detect and study them by the effect of matter near it. If a black hole passes through a cloud of interstellar matter, it will draw matter inward (this process is known as accretion). A similar process occurs when a star passes through a black hole. When this happens, a star can break apart as it pulls it self toward it. As the attracted matter accelerates and starts heating up, it emits x-rays that are radiate into space.
Recent studies do show that black do have a very big influence towards neighborhoods around it. The black hole emits gamma ray bursts, devouring nearby stars, and spurring the growth of new stars in some areas while stalling it in others.
Info: https://science.nasa.gov/astrophysics/focus-areas/black-holes
Hope this Helps! (:
Answer:
Amount of work done by Joanne = 80 joule
Explanation:
Given:
Displacement of ball = 2 meters
Force applied = 40 newtons
Find:
Amount of work done by Joanne
Computation;
Work done = Force applied x Displacement
Amount of work done by Joanne = Force applied x Displacement of ball
Amount of work done by Joanne = 40 x 2
Amount of work done by Joanne = 80 joule
Answer:
V = 2.8 m/s
Explanation:
It is given that,
Mass of falcon, ![m_1=4\ kg](https://tex.z-dn.net/?f=m_1%3D4%5C%20kg)
Mass of dove, ![m_2=1\ kg](https://tex.z-dn.net/?f=m_2%3D1%5C%20kg)
Initial velocity of falcon, ![u_1=3\ m/s](https://tex.z-dn.net/?f=u_1%3D3%5C%20m%2Fs)
Initial velocity of dove, ![u_2=2\ m/s](https://tex.z-dn.net/?f=u_2%3D2%5C%20m%2Fs)
When the falcon catches the dove, the momentum remains conserved. Using the formula for the conservation of momentum as :
![m_1u_1+m_2u_2=(m_1+m_2)V](https://tex.z-dn.net/?f=m_1u_1%2Bm_2u_2%3D%28m_1%2Bm_2%29V)
V is the velocity after impact
![V=\dfrac{m_1u_1+m_2u_2}{(m_1+m_2)}](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7Bm_1u_1%2Bm_2u_2%7D%7B%28m_1%2Bm_2%29%7D)
![V=\dfrac{4\times 3+1\times 2}{(4+1)}](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7B4%5Ctimes%203%2B1%5Ctimes%202%7D%7B%284%2B1%29%7D)
V = 2.8 m/s
So, their velocity after the impact is 2.8 m/s. Hence, this is the required solution.