Answer:
A
Explanation:
Instantaneous speed is the magnitude of instantaneous velocity
Answer: 2561.7 pounds
Explanation:
If we assume the total weight of an airplane (in pounds units) as a <u>linear function</u> of the amount of fuel in its tank (in gallons) and we make a Weight vs amount of fuel graph, which resulting slope is 5.7, we can use the slope equation of the line:
(1)
Where:
is the slope of the line
is the airplane weight with 51 gallons of fuel in its tank (assuming we chose the Y axis for the airplane weight in the graph)
is the fuel in airplane's tank for a total weigth of 2390.7 pounds (assuming we chose the X axis for the a,ount of fuel in the tank in the graph)
This means we already have one point of the graph, which coordinate is:
![(X_{1},Y_{1})=(51,2390.7)](https://tex.z-dn.net/?f=%28X_%7B1%7D%2CY_%7B1%7D%29%3D%2851%2C2390.7%29)
Rewritting (1):
(2)
As Y is a function of X:
(3)
Substituting the known values:
(4)
(5)
(6)
Now, evaluating this function when X=81 (talking about the 81 gallons of fuel in the tank):
(7)
(8) This means the weight of the plane when it has 81 gallons of fuel in its tank is 2561.7 pounds.
i would think by taking all the water out and storing it somewhere else and filtering it or cleaning it then put it back
Answer:
The final velocity of the second car is 57 m/s south.
Explanation:
This is an elastic collision between two train cars. In this case, the total kinetic energy between the two bodies will remain the same.
The formula to apply is :
![m_1v_1i +m_2v_2i=m_1v_1f+m_2v_2f](https://tex.z-dn.net/?f=m_1v_1i%20%2Bm_2v_2i%3Dm_1v_1f%2Bm_2v_2f)
where ;
![m_1=mass of object 1\\v_1i=initial velocity object1\\m_2=mass of object2\\v_2i=initial velocity object 2\\v_1f=final velocity object 1\\v_2f=final velocity object 2](https://tex.z-dn.net/?f=m_1%3Dmass%20of%20object%201%5C%5Cv_1i%3Dinitial%20%20velocity%20object1%5C%5Cm_2%3Dmass%20of%20object2%5C%5Cv_2i%3Dinitial%20velocity%20object%202%5C%5Cv_1f%3Dfinal%20velocity%20object%201%5C%5Cv_2f%3Dfinal%20velocity%20object%202)
Given in the question that;
![m_1=14650kg\\v_1i=18m/s\\m_2=3825kg\\v_2i=11m/s\\v_1f=6m/s\\v_2f=?](https://tex.z-dn.net/?f=m_1%3D14650kg%5C%5Cv_1i%3D18m%2Fs%5C%5Cm_2%3D3825kg%5C%5Cv_2i%3D11m%2Fs%5C%5Cv_1f%3D6m%2Fs%5C%5Cv_2f%3D%3F)
Apply the formula as;
![m_1v_1i +m_2v_2i=m_1v_1f+m_2v_2f](https://tex.z-dn.net/?f=m_1v_1i%20%2Bm_2v_2i%3Dm_1v_1f%2Bm_2v_2f)
{14650*18}+{3825*11} = {14650 *6} + {3825 * v₂f}
263700+42075=87900 + 3825v₂f
305775 =87900 + 3825v₂f
305775-87900 = 3825v₂f
217875=3825v₂f
217875/3825 =v₂f
56.96 = v₂f
<u>57 m/s = v₂f { nearest whole number}</u>