Answer:
The resulting coordinate is
Explanation:
From the question we are told that
The mass of the first dice is ![m_1 = 11.10 \ g](https://tex.z-dn.net/?f=m_1%20%3D%20%2011.10%20%5C%20g)
The mass of the second dice is ![m_2 = 15.10 \ g](https://tex.z-dn.net/?f=m_2%20%20%3D%20%2015.10%20%5C%20g)
The mass of the third dice is ![m_3 = 18.90 \ g](https://tex.z-dn.net/?f=m_3%20%3D%20%2018.90%20%5C%20g)
The coordinate of the first dice is ![(x_1, y_1) = (0.3150\ m , -0.4990 \ m )](https://tex.z-dn.net/?f=%28x_1%2C%20y_1%29%20%3D%20%20%280.3150%5C%20m%20%20%2C%20%20-0.4990%20%5C%20m%20%20%29)
The coordinate of the second dice is ![(x_2,y_2) = (-0.4050 \ m , 0.4850 \ m )](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%20%28-0.4050%20%20%5C%20m%20%20%2C%200.4850%20%5C%20m%20%20%29)
The coordinate of the third dice is ![(x_3 , y_3) = (-0.1150 \ m , -0.1850\ m )](https://tex.z-dn.net/?f=%28x_3%20%2C%20y_3%29%20%3D%20%20%28-0.1150%20%5C%20m%20%2C%20%20-0.1850%5C%20m%20%29)
Generally the resulting coordinate of the center of mass of the dice in the x-axis is mathematically evaluated as
![x\ cm = \frac{m_1 * x_1 + m_2 * x_2 + m_3 * x_3}{m_1 + m_2 +m_3 }](https://tex.z-dn.net/?f=x%5C%20cm%20%20%3D%20%20%5Cfrac%7Bm_1%20%2A%20x_1%20%2B%20m_2%20%2A%20x_2%20%2B%20m_3%20%2A%20x_3%7D%7Bm_1%20%2B%20m_2%20%2Bm_3%20%7D)
i.e the summation of the moments about their x-axis divided by the magnitude of their masses
substituting values
![x\ cm = \frac{11.0 * 0.3150 + 15.10 * (-0.4050) + 18.90 * (-0.1150)}{11.100 + 15.10 +18.90 }](https://tex.z-dn.net/?f=x%5C%20cm%20%20%3D%20%20%5Cfrac%7B11.0%20%20%2A%200.3150%20%2B%2015.10%20%2A%20%28-0.4050%29%20%2B%2018.90%20%2A%20%28-0.1150%29%7D%7B11.100%20%2B%2015.10%20%2B18.90%20%7D)
![x\ cm = -0.170 \ m](https://tex.z-dn.net/?f=x%5C%20cm%20%20%3D%20-0.170%20%5C%20m)
Generally the resulting coordinate of the center of mass of the dice in the y-axis is mathematically evaluated as
![y\ cm = \frac{m_1 * y_1 + m_2 * y_2 + m_3 * y_3}{m_1 + m_2 +m_3 }](https://tex.z-dn.net/?f=y%5C%20cm%20%20%3D%20%20%5Cfrac%7Bm_1%20%2A%20y_1%20%2B%20m_2%20%2A%20y_2%20%2B%20m_3%20%2A%20y_3%7D%7Bm_1%20%2B%20m_2%20%2Bm_3%20%7D)
![y\ cm = \frac{ 11.10 * (-0.4990) + (15.10) * (0.4850) + (18.90) * (-0.1850)}{ 11.10 + 15.10 +18.90 }](https://tex.z-dn.net/?f=y%5C%20cm%20%20%3D%20%20%5Cfrac%7B%2011.10%20%2A%20%28-0.4990%29%20%2B%20%2815.10%29%20%2A%20%280.4850%29%20%2B%20%2818.90%29%20%2A%20%28-0.1850%29%7D%7B%2011.10%20%2B%2015.10%20%2B18.90%20%7D)
![y\ cm = -0.038 \ m](https://tex.z-dn.net/?f=y%5C%20cm%20%20%3D%20%20-0.038%20%5C%20m)
Thus the resulting coordinate is ![(x,y) = (-0.170 \ m , -0.038 \ m )](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%20%28-0.170%20%5C%20m%20%20%2C%20%20-0.038%20%5C%20m%20%29)
We have: Fnet = m×a
Here, Fnet = 1860-480 = 1380 towards right
m = 230 Kg
Substitute their values into the expression:
1380 = 230 × a
a = 1380 / 230
a = 6 m/s² towards right
In short, Your Answer would be 6 m/s² towards right
Hope this helps!
Runner A is faster than runner B and Runner B has a head start.
<h3>What is a velocity time graph?</h3>
The velocity time graph shows us how fast that an object can be. The slope of the graph is the acceleration.
If we look at the graph as shown in the image attached to this answer, we can see that Runner A is faster than runner B and Runner B has a head start.
Learn more about velocity time graph:brainly.com/question/11290682
#SPJ1
Answer: 10 m/s
Given:
Force, F = 25 N
Initial velocity ![u=0 m/s^{2}](https://tex.z-dn.net/?f=u%3D0%20m%2Fs%5E%7B2%7D)
Distance moved, s= 4 m
mass, m = 2 kg
Formula Used:
![F = ma](https://tex.z-dn.net/?f=%20F%20%3D%20ma%20)
where a is the acceleration.
equation of motion:
![2as=v^{2}-u^{2}](https://tex.z-dn.net/?f=2as%3Dv%5E%7B2%7D-u%5E%7B2%7D)
First, we would calculate the acceleration from the formula for force.
![a= \frac{F}{m}=\frac{25}{2}m/s^{2}](https://tex.z-dn.net/?f=a%3D%20%5Cfrac%7BF%7D%7Bm%7D%3D%5Cfrac%7B25%7D%7B2%7Dm%2Fs%5E%7B2%7D)
Using the equation of motion, we can find the final velocity now:
×
×![4= v^{2}-0^{2}](https://tex.z-dn.net/?f=4%3D%20v%5E%7B2%7D-0%5E%7B2%7D)
taking the square root on both sides and ignoring the negative sign:
v= 10 m/s