Final answer:
To launch from the ground, a rocket must produce thrust at least equal to its weight. The fuel consumption rate needed for this can be calculated using the thrust equation with known values for rocket weight and exhaust velocity. The minimum rate for the given rocket is 1.250kg/sec.
Step-by-step explanation:
The subject matter of this question is rooted in physics, specifically in the domain of rocket propulsion mechanics. Using the conservation of momentum and the concept of thrust, we can calculate the minimum rate of fuel consumption needed for a rocket to take off.
For a rocket to overcome gravity and take off, the thrust produced by its engines should be at least equal to the weight of the rocket. The thrust, or the force that propels the rocket upwards, can be calculated using the formula: F = dm/dt * Ve, where 'dm/dt' is the rate of change of mass with time (rate of fuel consumption) and 'Ve' is the exhaust velocity of the fuel.
So to find the minimum fuel consumption rate needed, we rearrange the formula to give dm/dt = F/Ve. Substituting the given values, we find dm/dt = (200kg * 10m/s²) / 1.6 km/s = 1.25 kg/s. Therefore, the minimum rate of consumption of fuel so that the rocket may rise from ground is (a) 1.250kg/sec.
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