Answer:
R = 45.82[mm/s], with an angle of 48.95°
Explanation:
To solve this, the two vectors will be illustrated in a diagram, allowing someone viewing from outside the game board to see that the collective motion comes from both the marble's trajectory and the board's movement.
The image attached displays this vector addition. By utilizing the parallelogram law, we can derive the resultant vector, shown in red.
Next, we will break down the velocity vector of 40 [mm/s] into its x and y components.
x = 40*cos(60) = 20 [mm/s]
y = 40*sin(60) = 34.64 [mm/s]
<pConsequently, the resultant vector is:Rx = 20 + 10 = 30 [mm/s]
Ry = 34.64 [mm/s]
<pApplying the Pythagorean theorem, we can ascertain the vector’s magnitudeNext, we can calculate the angle relative to the horizontal using the previously obtained components.
tan α = 34.46 / 30
α = 48.95°
Answer:
The total energy can be expressed as
Explanation:
The problem states that
The Poynting vector, which measures energy flux, equals
The rectangle's length is represented by
The width of the rectangle is
The duration considered is
Mathematically, the overall electromagnetic energy incident on the area is given by
where A denotes the area of the rectangle, calculated as
By plugging in the respective values
Again substituting values
Answer:
The final size is nearly the same as the initial size because the increase in size is remarkably small
Solution:
According to the problem:
The proton beam energy is E = 250 GeV =
Distance traveled by the photon, d = 1 km = 1000 m
Proton mass,
Initial size of the wave packet,
Now,
This operates under relativistic principles
The rest mass energy for the proton is expressed as:
This proton energy is
Thus, the speed of the proton, v
The time to cover 1 km = 1000 m of distance is calculated as:
T =
T =
According to the dispersion factor;
Thus, the widening of the wave packet is relatively minor.
Hence, we can conclude that:
where
= final width