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An astronaut exploring a distant solar system lands on an

Chapter 12, Problem 72GP

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QUESTION:

Problem 72GP

An astronaut exploring a distant solar system lands on an unnamed planet with a radius of 3860 km. When the astronaut jumps upward with an initial speed of 3.10 m/s, she rises to a height of 0.580 m. What is the mass of the planet?

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QUESTION:

Problem 72GP

An astronaut exploring a distant solar system lands on an unnamed planet with a radius of 3860 km. When the astronaut jumps upward with an initial speed of 3.10 m/s, she rises to a height of 0.580 m. What is the mass of the planet?

ANSWER:

Step 1 of 3

An astronaut landed on a planet with the radius R and she jumps upward with the initial speed \(\mathrm{V}_{\mathrm{0}}\) and reaches a height \(\Delta \mathrm{x}\). We are going to find the mass of the planet using the data given.

The radius of the planet \(\mathrm{R}=3860 \mathrm{\ km}=3.86 \times 10^{6} \mathrm{\ m}\)

The gravitational constant G = 6.67 x 10-11 N m2/kg2

The initial speed of the astronaut \(\mathrm{v}_{0}=3.10 \mathrm{\ m} / \mathrm{s}\)

The height reached \(\Delta \mathrm{x}=0.580 \mathrm{\ m}\)

The final speed at the given height v = 0

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