Question 1158791
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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 ln 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 24​, an exhaust velocity of 2.8 ​km/s, and a firing time of 20 s. 
Can the spacecraft achieve a stable orbit 300 km above​ Earth?
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<pre>
To solve the problem, we substitute the given numbers t = 20 seconds, c = 2.8 km/s, R = 24 into the given formula 
and calculate

     v = -0.0098*20 + 2.8*ln(24) = 8.702550725 km/s for the rocket speed.


It is greater than 7.7 kilometers per second, so, according to the context, the spacecraft can achieve a stable orbit.
</pre>

Solved.