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:
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.
Acceleration is the rate of change of velocity, so can be calculated by:
a = v2 - v1 / t where v2 and v1 are the final and initial velocities of the object respectively and t is the time taken. Therefore the acceleration is:
a = 30 m/s - 20 m/s / 2.0 s = 10 m/s / 2.0 s = 5 m/(s^2)
Hope this helps!
Answer:
Explanation:
Kinetic energy at the height = 1/2 m v²
= 1/2 x 750 x 20²
= 150000 J
Its potential energy = mgh
= 750 x 9.8 x 5
=36750 J
Total energy = 186750 J
Its total kinetic energy will be equal to 186750 J , according to conservation of mechanical energy
If v be its velocity at the bottom
1/2 m v² = 186750
v = √498
= 22.31 m /s
Kepler's first law - sometimes referred to as the law of ellipses - explains that planets are orbiting the sun in a path described as an ellipse. An ellipse can easily be constructed using a pencil, two tacks, a string, a sheet of paper and a piece of cardboard. Tack the sheet of paper to the cardboard using the two tacks. Then tie the string into a loop and wrap the loop around the two tacks. Take your pencil and pull the string until the pencil and two tacks make a triangle (see diagram at the right). Then begin to trace out a path with the pencil, keeping the string wrapped tightly around the tacks. The resulting shape will be an ellipse. An ellipse is a special curve in which the sum of the distances from every point on the curve to two other points is a constant. The two other points (represented here by the tack locations) are known as the foci of the ellipse. The closer together that these points are, the more closely that the ellipse resembles the shape of a circle. In fact, a circle is the special case of an ellipse in which the two foci are at the same location. Kepler's first law is rather simple - all planets orbit the sun in a path that resembles an ellipse, with the sun being located at one of the foci of that ellipse.
Answer: 4.50*10^-6T (0.00000450071T)
Explanation: A current carrying conductor has been knowing to generate a specific amount of magnetic field.
This is given by the Bio-savart law (mathematical).
The Bio-savart law is a mathematical equation that gives the value of strength of the magnetic field created by a current carrying conductor.
B=(Uo* I) /2πr
Where
B= strength of magnetic field
Uo = magnetic permeability in free space = 1.257 *10^-6
r = distance between current carrying conductor and any reference point.
By doing the neccesary algebra, we have
B=(1.257 *10^-6 * 180)/ (2 * 3.142 * 8)
B= 2.2626 *10^-4 / 50.2857
B=4.5 * 10^-6T (0.00000450071T)
