find the minimum rate at which the fuel must be consumed by a rocket so as to be able to take of vertically. Given that the total mass at the time of takeoff is 3000 kg and the velocity of fuel expense is 300 metre per second. (g=9.8m/s^2)
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PHYSICS
A rocket, set for vertical launching, has a mass of 50 kg and contains 450 kg of fuel. It can have a maximum exhaust speed of 2 km s
−1
. If g=10 ms
−2
, what should be the minimum rate of fuel consumption to just lift it off the launching pad?
A .
2.5 kg s
−1
B .
5 kg s
−1
C .
7.5 kg s
−1
D .
10 kg s
−1
December 20, 2019
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Shivu Chandaria
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ANSWER
We have mass of rocket = 50 kg and mass of fuel = 450 kg
Thus total mass = 500 kg
Exhaust speed of rocket v
r
= 2 km/s = 2×10
3
m/s
Force = mass×gravity = 500×10m/s=5000 N
Also we know force of an object = mass×
t
v
as initial velocity = 0
So F=v
r
×
dt
dm
where
dt
dm
is the rate of fuel burn.
dt
dm
=
v
r
F
=
2000
5000
=2.5 kg /s