Please do problem (b) thanks Conceptualize Imagine projecting the spacecraft fro

Question

Please do problem (b) thanks

Conceptualize Imagine projecting the spacecraft from the Earth's surface so that it moves farther and farther away, traveling more and more slowly, with its speed approaching zero. Its speed will never reach zero, however, so the object will never turn around and come back. Categorize This example is a substitution problem. Use the equation to find the escape speed: V_esc = squareroot 2GM_E/R_E = squareroot 2(6.674 times 10^-11 N middot m^2/kg^2) (5.97 times 10^24 kg)/6.37 times 10^6 m = 11184.73113 m/s Evaluate the kinetic energy of the spacecraft from the equation: K = 1/2 mv^2_esc = 1/2 (4.8 times 10^3 kg) V^2_esc = 300235709600 J The calculated escape speed corresponds to about 25,000 mi/h. The kinetic energy of the spacecraft is equivalent to the energy released by the combustion of about 2, 300 gal of gasoline. Suppose the rocket was initially on a circular orbit around Earth with a period of 1.4 days. (a) What is its orbital speed? 2744.95 m/s (b) If we want to propel a portion of the rocket to infinity (in the direction tangential to the circular orbit), what's the escape speed from there? 2767.89 This is the speed to maintain the orbit, rather than the escape speed. Calculate the speed at which the rocket has the energy it takes to escape its orbit. m/s

Explanation / Answer

Given

The orbital velocity Vorbit = 2744.95 m/s

Solution

The escape velocity Ve = 2 x Vorbit

Ve = 1.414 x 2744.95

Ve = 3881.95 m/s

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