Two resistors ( 3 ohms & 6 ohms) in a series circuit with a power supply = 12 volts. The current through resistor 6 ohms is

Answer:

The BMX rider lands 5.4 meters horizontally away from the ramp's end.

Explanation:

The BMX position vector is represented as:

r = (x0 + v0 × t × cos α, y0 + v0 × t × sin α + ½ × g × t²)

Where:

r = position at time t

x0 = initial horizontal position

v0 = initial speed

α = angle of jump

y0 = initial vertical height

g = gravitational acceleration (-9.8 m/s², upward positive)

Refer to the diagram for clarity. At the landing time, the vertical coordinate of the position vector is -2.4 m, measured from the ramp's edge as the origin. Using the vertical component equation for y, one can solve for t, then substitute t to find the horizontal distance.

The vertical position equation:

-2.4 m = 0 + 5.9 m/s × t × sin 40° - ½ × 9.8 m/s² × t²

Rearranged:

0 = -4.9 t² + 5.9 t × sin 40° + 2.4

Solving this quadratic yields:

t = 1.2 seconds

Then, calculate horizontal distance:

x = 0 + 5.9 m/s × 1.2 s × cos 40° = 5.4 m

This means the BMX lands 5.4 meters from the ramp's edge.

Have a great day!

This involves circuit analysis through simplification of the resistors and capacitors. We need to determine the time constant for each circuit in figures A, B, C, D, and E. This leads to ranking the duration the bulbs remain lit from longest to shortest based on each circuit's time constant. The ranking for the time constants is C > A = E > B > D. Capacitance plays a pivotal role in electrostatics, and devices called capacitors are vital components in electronic circuits. When more charge is applied to a conductor, the voltage escalates proportionately. The capacitance of a conductor is quantified as C = q/v. Adding resistors in series raises resistance while parallel configurations reduce it, conversely increasing capacitance in parallel and diminishing it in series. Thus, circuits with greater time constants take longer to discharge.

Answer:

This assertion is inaccurate.

Explanation:

The random nature of gas molecules results in their erratic motion and occasional collisions. While it is true that they tend to avoid being tightly packed, achieving the maximum separation from each other is not always feasible due to their lack of fixed positions. Consequently, gas molecules in a container cannot consistently maintain the furthest distance from their neighboring molecules.

In contrast, the separation among electrons is primarily influenced by repulsive forces, not random movement as in gases. Electrons maintain distance as a result of repulsion between similarly charged particles. Therefore, the arrangement of electrons on a charged copper sphere occurs not from a random distribution but rather due to repulsion, establishing a set distance between them.

The alteration in potential energy is  

In the query, it is stated that

  The intensity of the uniform electric field equals

     The distance the electron covers is  

Typically, the force exerted on this electron is expressed mathematically as

     

Where F signifies the force and  q represents the charge of the electron, which is a fixed value of

    Thus  

     

     

Generally, the work-energy theorem is mathematically framed as

         

Where W denotes the work done on the electron by the electric field and    is the change in kinetic energy

Additionally, work done on the electron can also be described as

       

Where   assuming that the electron's movement aligns with the x-axis  

        So

             

Inserting values

         

         

According to the conservation of energy

       

Where signifies the change  in  potential energy  

Thus