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The radius of Venus (from the center to just above the atmosphere) is 6050 km (6050✕103 m), and its mass is 4.9✕1024 kg. An object is launched straight up from just above the atmosphere of Venus. (a) What initial speed is needed so that when the object is far from Venus its final speed is 8000 m/s? vinitial = m/s (b) What initial speed is needed so that when the object is far from Venus its final speed is 0 m/s? (This is called the "escape speed.") vescape = m/s

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Answer:

(a) The initial speed required is 13116 m/s

(b) The escape speed is 10394 m/s

This problem involves the application of newtons laws of gravitation. The forces in action here are conservative and as a result mechanical energy is conserved.

The full calculation can be found in the attachment below.

Explanation:

In both parts (a) and (b) the energy conservation equation were used. Assumption was made that when the object is very far from the planet the distance from the planet's center approaches infinity and the gravitational potential energy approaches zero.

The calculation can be found below.

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