Which of these nebulae is the odd one out?

Answer:

A) 328 m

B) 80.22 m/s

C) 8.18 sec

Explanation:

A)

The rocket's initial acceleration is 2.25 m/s²

Time until engine failure is 15.4 s

Initial velocity u during takeoff = 0 m/s

Distance covered while the engine is functional =?

We apply Newton's laws for this calculation

S = ut + a

Here, S represents the distance traveled under the rocket's thrust

S = (0 x 15.4) + (2.25 x )

S = 0 + 266.81 m = 266.81 m

Before the engine fails, the final velocity can be found using:

v = u + at

v = 0 + (2.25 x 15.4) = 34.65 m/s

Once the engine fails, the rocket decelerates under gravitational pull at g = -9.81 m/s²  (acting downwards)

The upward initial velocity when freefall begins is v = 34.65 m/s

The final velocity is reached at peak height, where the rocket halts, therefore:

u = 0 m/s

The distance covered during this freefall will be s =?

Utilizing the equation

= + 2gs

= + 2(-9.81 x s)

0 = 1200.6 - 19.62s

-1200.6 = -19.62s

s = -1200.6/-19.62 = 61.19 m

Thus,

Maximum Height = 266.81 m  + 61.19 m =  328 m

B)

At maximum height, the rocket’s initial upward velocity drops to 0 m/s (the rocket completely stops)

The descent occurs freely under g = 9.81 m/s² (acting downwards)

The distance covered during the fall will be 328 m

Final velocity v just prior to impact =?

Applying = + 2gs

= + 2(9.81 x 328)

= 0 + 6435.36

v = = 80.22 m/s

The time taken before reaching the pad is found as follows

v = u + gt

80.22 = 0 + 9.81t

t = 80.22/9.81 = 8.18 sec

The fundamental equation is derived from Mr. Planck: E=h \nu, where h is Planck’s constant and ν is the frequency. This relationship describes the energy per photon at a specific frequency. Although a wavelength is provided, it can easily be converted to frequency using the equation: c= lambda / nu, where c denotes the speed of light; λ (lambda) is the wavelength; and ν is the frequency. Once the energy of a photon with a wavelength of 550nm is determined, it will show how many photons are needed to gather 10^-18J. Remember to pay attention to the units.

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 greatest mass that can hang without submerging is 2.93 kg. The provided details are as follows: sphere diameter = 20 cm, hence the radius r = 10 cm = 0.10 m. The density of the Styrofoam sphere is 300 kg/m³. The sphere's volume calculates to 4.18 * 10⁻³ m³. Mass M = Density * Volume results in (300)(4.18 * 10⁻³ m³) = 1.25 kg. The displaced water mass is computed as volume * water density, yielding 4.18 * 10⁻³ m³ * 1000 = 4.18 kg. The additional mass the sphere can hold is the difference between the two mass calculations: 4.18 kg - 1.25 kg = 2.93 kg.

Answer:

 = 3289.8 m/s

Explanation:

This problem can be approached using momentum definitions.

     I = ∫ F dt

We substitute and compute.

     I = ∫ (at - bt²) dt

Integrating gives us:

      I = a t² / 2 - b t³ / 3

We will evaluate between the limits I=0 for t = 0 ms and higher I=I for t = 2.74 ms:

      I = a (2.74² / 2- 0) - b (2.74³ / 3 -0)

      I = a 3.754 - b 6.857

Substituting the values for a and b, we find:

      I = 1500 3.754 - 20 6.857

      I = 5,631 - 137.14

      I = 5493.9 N s

Next, we engage the relationship between impulse and momentum:

      I = Δp = m - m v₀o

      I = m - 0

       = I / m

     = 5493.9 /1.67

     = 3289.8 m/s