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iren [92.7K]
3 years ago
15

A rocket accelerates by burning its onboard fuel, so its mass decreases with time. Suppose the initial mass of the rocket at lif

toff (including its fuel) is m, the fuel is consumed at rate r, and the exhaust gases are ejected with constant velocity ve (relative to the rocket). A model for the velocity of the rocket at time t is given by the equation:
v(t)=−gt−velnm−rtm


Where g is the acceleration due to gravity and t is not too large?If g=9.8m/s2, m=29,000kg, r=170kg/s, and ve=2,900m/s.

What would the height of the rocket be one minute after liftoff?
Physics
1 answer:
Serggg [28]3 years ago
4 0

Answer:

Height of the rocket be one minute after liftoff is 40.1382 km.

Explanation:

v(t)=-gt-v_e\times \ln \frac{m-rt}{m}

v = velocity of rocket at time t

g = Acceleration due to gravity =9.8 m/s^2

v_e = Constant velocity relative to the rocket = 2,900m/s.

m = Initial mass of the rocket at liftoff = 29000 kg

r = Rate at which fuel is consumed = 170 kg/s

Velocity of the rocket after 1 minute of the liftoff =v

t = 1 minute = 60 seconds'

Substituting all the given values in in the given equation:

v(60)=-9.8 m/s^2\times 60 s-2,900m/s\times \ln (\frac{29,000 kg-170 kg/s\times 60 s}{2,9000 kg})

v(60) = 668.97 m/s

Height of the rocket = h

Velocity=\frac{Displacement}{time}

668.97 m/s=\frac{h}{60 s}

h=668.97 m/s\times 60 s=40,138.2 m = 40.1382 km

Height of the rocket be one minute after liftoff is 40.1382 km.

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3 0
1 year ago
The period of a carrier wave is T=0.01 seconds. Determine the frequency and wavelength of the carrier wave. a. f=10 Hz, λ=3E8 me
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Explanation:

It is given that,

The period of the carrier wave, T = 0.01 s

Let f and \lambda are frequency and the wavelength of the wave respectively. The relationship between the time period and the frequency is given by :

f=\dfrac{1}{T}

f=\dfrac{1}{0.01}

f = 100 Hz

The wavelength of a wave is given by :

\lambda=\dfrac{c}{f}

\lambda=\dfrac{3\times 10^8}{100}

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A bicyclist of mass 112 kg rides in a circle at a speed of 8.9 m/s. If the radius of the circle is 15.5 m, what is the centripet
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The centripetal force, Fc, is calculated through the equation, 
                                    Fc = mv²/r
where m is the mass,v is the velocity, and r is the radius. 
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                                     Fc = (112 kg)(8.9 m/s)² / (15.5 m)
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S Problem Set<br> 2.) 6.4 x 109 nm to cm
anyanavicka [17]

Answer:

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Now we can convert from metres to centimetres, keeping in mind that

1 m = 10^2 cm

So, we find:

6.4 m \cdot 10^2 cm/m = 6.4\cdot 10^2 cm

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