document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158791>Question 1158791</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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? </SPAN>\n" );
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document.write( "A spacecraft can attain a stable orbit 300 kilometers above Earth if it reaches a velocity of 7.7 kilometers per second. <BR>\n" );
document.write( "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 <BR>\n" );
document.write( "in​ seconds, c is the velocity of the exhaust in kilometers per​ second, and R is the ratio of the mass of the rocket <BR>\n" );
document.write( "filled with fuel to the mass of the rocket without fuel. Find the velocity of a spacecraft whose booster rocket <BR>\n" );
document.write( "has a mass ratio of 24​, an exhaust velocity of 2.8 ​km/s, and a firing time of 20 s. <BR>\n" );
document.write( "Can the spacecraft achieve a stable orbit 300 km above​ Earth?<BR>\n" );
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document.write( "To solve the problem, we substitute the given numbers t = 20 seconds, c = 2.8 km/s, R = 24 into the given formula \r\n" );
document.write( "and calculate\r\n" );
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document.write( "     v = -0.0098*20 + 2.8*ln(24) = 8.702550725 km/s for the rocket speed.\r\n" );
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document.write( "It is greater than 7.7 kilometers per second, so, according to the context, the spacecraft can achieve a stable orbit.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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