Answer:
<u><em>note:</em></u>
<u><em>solution is attached due to error in mathematical equation. please find the attachment</em></u>
Answer:
rm = 38280860.6[m]
Explanation:
We can solve this problem by using Newton's universal gravitation law.
In the attached image we can find a schematic of the locations of the Earth and the moon and that the sum of the distances re plus rm will be equal to the distance given as initial data in the problem rt = 3.84 × 108 m
Now the key to solving this problem is to establish a point of equalisation of both forces, i.e. the point where the Earth pulls the astronaut with the same force as the moon pulls the astronaut.
Mathematically this equals:
When we match these equations the masses cancel out as the universal gravitational constant
To solve this equation we have to replace the first equation of related with the distances.
Now, we have a second-degree equation, the only way to solve it is by using the formula of the quadratic equation.
We work with positive value
rm = 38280860.6[m] = 38280.86[km]
Answer:
The magnetic field through the wire must be changing
Explanation:
According to Faraday's law, the induced emf, ε in a metallic conductor is directly proportional to the rate of change of magnetic flux,Φ through it. This is stated mathematically as ε = dΦ/dt.
Now for the wire, the magnetic flux through it is given by Φ = ABcosθ where A = cross-sectional area of wire, B = magnetic field and θ = angle between A and B.
So, dΦ/dt = dABcosθ/dt
Since A and B are constant,
dΦ/dt = ABdcosθ/dt = -(dθ/dt)ABsinθ
Since dθ/dt implies a change in the angle between A and B, since A is constant, it implies that B must be rotating.
So, <u>for an electric current (or voltage) to be produced in the wire, the magnetic field must be rotating or changing</u>.
Answer:
A) The acceleration is zero
<em>B) The total distance is 112 m</em>
Explanation:
<u>Velocity vs Time Graph</u>
It shows the behavior of the velocity as time increases. If the velocity increases, then the acceleration is positive, if the velocity decreases, the acceleration is negative, and if the velocity is constant, then the acceleration is zero.
The graph shows a horizontal line between points A and B. It means the velocity didn't change in that interval. Thus the acceleration in that zone is zero.
A. To calculate the acceleration, we use the formula:
Let's pick the extremes of the region AB: (0,8) and (12,8). The acceleration is:
This confirms the previous conclusion.
B. The distance covered by the body can be calculated as the area behind the graph. Since the velocity behaves differently after t=12 s, we'll split the total area into a rectangle and a triangle.
Area of rectangle= base*height=12 s * 8 m/s = 96 m
Area of triangle= base*height/2 = 4 s * 8 m/s /2= 16 m
The total distance is: 96 m + 16 m = 112 m