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Sagot :
103.4 kg mass of fuel is needed to reach a top speed of 4000 m/s .
What is speed ?
The speed at which an object's location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Since speed only has a direction and no magnitude, it is a scalar quantity.
Let fuel is released at the rate of dm / dt where m is mass of the fuel
thrust created on rocket
= d ( mv ) / dt
= v dm / dt
this is equal to force created on the rocket
= 220 dv / dt
so applying newton's law
v dm / dt = 220 dv / dt
v dm = 220 dv
dv / v = dm / 220
integrating on both sides
∫ dv / v = ∫ dm / 220
lnv = ( m₂ - m₁ ) / 220
ln4000 - ln 2500 = ( m₂ - m₁ ) / 220
( m₂ - m₁ ) = 220 x ( ln4000 - ln 2500 )
( m₂ - m₁ ) = 220 x ( 8.29 - 7.82 )
= 103.4 kg .
Complete question: A rocket in deep space has an empty mass of 220 kg and exhausts the hot gases of burned fuel at 2500 m/s. What mass of fuel is needed to reach a top speed of 4000 m/s.
To learn more about speed visit:https://brainly.com/question/28224010
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