Answer:
= 1,386 m / s
Explanation:
The mechanism behind rocket propulsion is defined by the formula
- v₀ = 
ln (M₀ / Mf)
Here, v refers to the initial, final, and relative velocities, while M indicates the masses
The provided values include the relative velocity (see = 2000 m / s) and the initial mass, where the mass of the rocket when loaded is represented as (M₀ = 5Mf)
For our analysis, we assume the rocket begins at rest (v₀ = 0)
Once half of the fuel has burnt, the mass ratio indicates that the current mass is
M = 2.5 Mf
- 0 = 2000 ln (5Mf / 2.5 Mf) = 2000 ln 2
= 1,386 m / s
The tension calculated is 236 N. The formula for tension is T = mg + ma. With the following values: m = 20 kg, g = 9.8 m/s², and a = 2.0 m/s², we find T = m(g + a) = 20(9.8 + 2.0) = 20(11.8) = 236 N.
The frequency detected is 394 Hz. This question pertains to the Doppler effect, outlined by the equation fo = {c + vo}/{c - vs} × f. Here, fo is the observed frequency, c denotes sound speed at 345 m/s, vo is the observer's velocity of 9.5 m/s, and vs refers to the source's velocity of -9.5 m/s (the negative indicates opposite directions). The source's frequency is given as 394 Hz. Substituting the values leads to fo = {345 + 9.5}/{345 + 9.5} × 394. Simplifying yields fo = (354.5/354.5) × 394 = 1 × 394 = 394 Hz.
Answer: The correct choice is (d) 
Explanation:
This analysis assumes that the heat supplied by the hot body matches the heat absorbed by the cold body.
where,
= the specific heat capacity of copper = 
= the specific heat capacity of water = 
= the mass of copper = 120 g
= the mass of water = 300 g
= the final temperature of the mixture = 
= the initial temperature of copper =?
= the initial temperature of water = 
Using the provided values in the equation yields:
Thus, the temperature of the kiln is approximately
To determine stress, we utilize the formula Stress = Force / Area. In this scenario, the force exerted by a person weighing 85 kg on the stool is calculated as F = mg = 85 kg * 9.8 m/s² = 833 N. Next, we find the total area of the three legs: A = 3 π (D/2)² = 3 π (2.5 x 10^-2 / 2)² = 1.4726 x 10^-3 m². Substituting into the equation gives Stress = 833 N / 1.4726 x 10^-3 m² = 5.656 x 10^5 N/m². To find strain, we apply the formula strain = Stress / Young’s modulus, with wood having Y = 1.3 x 10^10 N/m². Thus, strain = 5.656 x 10^5 N/m² / 1.3 x 10^10 N/m² = 4.35 x 10^-5 = 0.00435%.
This indicates that the legs will shorten by 0.00435%
