# A spacecraft can attain a stable orbit 300 kilometers above Earth if it reaches a velocity of 7.7 kilometers per second. The formula for

###### Question:

A spacecraft can attain a stable orbit 300 kilometers above Earth if it reaches a velocity of 7.7 kilometers per second. The formula for a rocket's maximum velocity v in kilometers per second is v= -0.0098t + c In R, where t is the firing time in seconds, c is the velocity of the exhaust in
kilometers per second, and R is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. Find the velocity of a
spacecraft whose booster rocket has a mass ratio of 25, an exhaust velocity of 2.9 km/s, and a firing time of 20 s. Can the spacecraft achieve a
stable orbit 300 km above Earth?

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