If someone can help me with these questions id greatly appreciate it 1) A 125,00

Question

If someone can help me with these questions id greatly appreciate it

1) A 125,000 space craft is landing on the moon (g = 1.6 m/s^2) using a rocket engine thrust that expels its exhaust at 20,000 m/s. At what rate must it consume its fuel to achieve an upward acceleration of 0.4 m/s^2?

2) How fast must a satellite move in a perfectly circular orbit of radius 15,000,000 meters assuming the Earth’s gravity is the only force acting on it? The mass of the Earth is 5.9 x 10^24 kg.

3)A block of mass 80.0 kg compresses a spring of spring constant 250 N/m by an amount ?x1 on a horizontal frictionless surface. It is then released to slide across the frictionless surface, 2.0 m up a ramp to a second horizontal surface with a coefficient of kinetic friction 0.3 where it comes to a stop after sliding 15.0 m. What was the initial compression of the spring ?x1?

Explanation / Answer

2.

r=15000000 m , M= 5.9*10^24 kg

Use Newton’s 2nd law

Fnet=ma

GMm/r^2=mv^2/r

GM/r=v^2

v=sqrt[GM/r]

Plugging values,

v=sqrt[(6.67*10^-11*5.9*10^24)/(15000000)]

v=5122.4 m/s

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