Newton's Law of Gravity question

[cyspope]

Homework Statement

An astronaut lands on an unknown planet with a radius of 3560 m. When she jumps upward with an initial speed of 3.00m/s she rises to a height of 0.50 m. What is the mass of the planet?

Homework Equations

v_f² = v₀² + 2a$$\Delta$$X

The Attempt at a Solution

In order to find the acceleration(gravity of the planet in this case) of the astronaut, I used following formula.

v_f² = v₀² + 2a$$\Delta$$X

If I solve for 'a', then I get

a = (v_f²-v_o²) / 2$$\Delta$$X

I pluged in the numbers,

a = (9m/s) / 2(0.5 m) = 9 m/s²

which doesn't make sense because the radius of the planet is only 3560 m.

please help me what to do next.

 

[jambaugh]

Homework Statement

An astronaut lands on an unknown planet with a radius of 3560 m. When she jumps upward with an initial speed of 3.00m/s she rises to a height of 0.50 m. What is the mass of the planet?

Homework Equations

v_f² = v₀² + 2a$$\Delta$$X

The Attempt at a Solution

In order to find the acceleration(gravity of the planet in this case) of the astronaut, I used following formula.

v_f² = v₀² + 2a$$\Delta$$X

If I solve for 'a', then I get

a = (v_f²-v_o²) / 2$$\Delta$$X

I pluged in the numbers,

a = (9m/s) / 2(0.5 m) = 9 m/s²

which doesn't make sense because the radius of the planet is only 3560 m.

please help me what to do next.

Newton's law of gravitation gives the acceleration at a given radius from the center of a given spherical mass. You have the acceleration and the radius so find the mass.

Remember the density needn't be the same as Earth's if that is what worries you. Maybe the planet has more metal in its core.

 

[Doc Al]

I pluged in the numbers,

a = (9m/s) / 2(0.5 m) = 9 m/s²

which doesn't make sense because the radius of the planet is only 3560 m.

Why doesn't it make sense?

Hint: You found the acceleration due to gravity on the surface of the planet. How does that relate to the mass and radius of the planet?

 

[cyspope]

thank you everyone