Answer:
7.166 hours = 430 minutes.
Explanation:
As both trains are approaching each other on the same track, their relative speed is the sum of their individual speeds. Hence, the time until they intersect (and inevitably collide) is determined by how long it takes for speeds of 65 mph and 55 mph to cover the total distance of 860 miles. One train will cover part of the distance, while the other will cover the remainder. To calculate the required time, we can apply the formula:
1 hour ---> 120 miles
X ----> 860 miles; hence X = (860 miles * 1 hour)/120 miles = 43/6 hours = 7.16666 hours. To convert this into minutes, recall that 1 hour equals 60 minutes; therefore, 43/6 hours * 60 minutes/hour = 430 minutes.
F = π/4 ρ d² v²
Explanation:
The formula for force is mass multiplied by acceleration:
F = ma
Acceleration is defined as the change in velocity over the change in time:
F = m Δv / Δt
Since there is no rebound effect, Δv is equal to v.
F = m v / Δt
Mass can be calculated as density multiplied by volume:
F = ρ V v / Δt
Flow rate describes the volume per time:
F = ρ Q v
Flow rate is determined by velocity multiplied by the cross-sectional area:
F = ρ (v A) v
This simplifies to F = ρ A v²
The area of a circle is calculated as pi times the square of the radius, or as pi/4 times the diameter squared:
F = ρ (π/4 d²) v²
Hence, F = π/4 ρ d² v²
Answer:
The separation between Earth and the star is growing.
Explanation:
When we witness the electromagnetic radiation of an object shifting towards the blue spectrum, it indicates that the object is moving closer, which compresses the light waves and decreases the wavelength towards blue, referred to as blueshift.
Conversely, when an object retreats from us rapidly, its light waves are stretched, resulting in a longer wavelength that shifts towards the red part of the spectrum. This shift is termed redshift.
The alteration of wavelength and frequency due to relative motion (approaching or receding) is explained by the Doppler effect.
In this case, since the light we detect from the star has transitioned to the red part of the spectrum, we can infer that it is moving away from Earth, indicating that the distance between the star and Earth is increasing.
Power is defined as the speed at which work is performed on an object. Like all rates, power is measured in relation to time. It reflects how quickly a task is completed. Two identical tasks can be executed at varying speeds - one slower and the other faster. The equation P = Fv can be used, where P symbolizes power, F denotes force, and V represents average velocity. Calculating the average velocity gives us V = P/F, or V = (5.8 x 10^4 W) / (2.1 x 10^4 N), resulting in V = 2.8 m/s.
Since the absolute values of the charges are identical, the changes in potential energy remain equivalent. Consequently, the changes in kinetic energy will also match. We have:
1 = Ke/Kp = m_e * v_e^2 / m_p * v_p^2, which simplifies to:
v_e/v_p = sqrt(m_p/m_e),
indicating that the velocity of the electron is sqrt(m_p/m_e) times greater than that of the proton.
