An empty spacecraft weighs 250,000 N on earth and carries 700,000 N of propellant. The spacecraftlands on Mercury, where the acceleration due to gravity is 3.7 m/s2. If the craft used 2/3 of its fuelmass to get to Mercury, how much thrust (in Newtons) will be required to lift-off from the planetif the minimum thrust is equal to the spacecraft weight?

The total thrust is 182482.96 N

Explanation:

Given:

empty spacecraft weight = 250000 N

m = mass of spacecraft = 250000/9.8 = 25510.2 kg

mass of propellant = 700000/9.8 = 71428.57 kg

remaining mass of propellant = 71428.57 - (2/3)*71428.57 = 23809.52 kg

The total mass is:

mtotal = 25510.2 + 23809.52 = 49319.72 kg

The total thrust is:

Ttotal = 49319.72 * 3.7 = 182482.96 N

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explanation:

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach