Calculate Mass of Unknown Planet with Physics B Ques.

[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

d = rt
x = x₀ + v₀t + \frac{1}{2}at²
M = gr² / G

The Attempt at a Solution

0.5 m / (3.0m/s) = \frac{1}{6}s
0.5 = 0 + 3\frac{1}{6}s + \frac{1}{2}a\frac{1}{6}²
0.5 = \frac{1}{2} + \frac{1}{2}a\frac{1}{36}
a = 0 m/s²?

I have no idea what to do. please help me.

 

[Delphi51]

You need to get the value of the acceleration from the information given about the motion of the astronaut. Look for an accelerated motion formula with distance but not time in it. Put in the numbers and solve for a.

Your calc getting 1/6 second looks like a d = vt, which does not apply to accelerated motion.

 

[cyspope]

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

v_f² = v₀² + 2a\DeltaX

If I solve for 'a', then I get

a = (v_f²-v_o² / 2\DeltaX

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.

 

[Delphi51]

I got 9, too. Maybe it is a neutron star or something.
Use this value of g to find M. Your formula M = gr2 / G should do it.