Mass and Radius of a Planet given v

[chitoboy18]

Homework Statement

While visiting Planet Physics, you toss a rock straight up at 13m/s and catch it 2.7s later. While you visit the surface, your cruise ship orbits at an altitude equal to the planet's radius every 210min . What is the mass and radius of the planet Physics?

Homework Equations

M=v^2r/G M=4pi^2r^3/GT^2

Please help me, I'm like so confused.

 

[Jonathan Scott]

Homework Statement

While visiting Planet Physics, you toss a rock straight up at 13m/s and catch it 2.7s later. While you visit the surface, your cruise ship orbits at an altitude equal to the planet's radius every 210min . What is the mass and radius of the planet Physics?

Homework Equations

M=v^2r/G M=4pi^2r^3/GT^2

Please help me, I'm like so confused.

You should not expect much help until you've tried a bit harder yourself.

You have two pieces of information, each of which gives you an equation to solve. When you've done that, you can substitute one in the other to get the answers. You also need $s = ut + \frac{1}{2} at^2$ for the first bit, and you need to work out how the orbit period relates to the speed and radius of orbit.

 

[baba89]

Based on the given information, we can use the equations M=v^2r/G and M=4pi^2r^3/GT^2 to calculate the mass and radius of Planet Physics.

First, we need to determine the gravitational constant, G, which is a fundamental constant of nature and is approximately equal to 6.67 x 10^-11 Nm^2/kg^2.

Next, we can use the equation M=v^2r/G to calculate the mass of the planet. Plugging in the given velocity of 13m/s and the time of 2.7s, we get M=(13m/s)^2*r/6.67 x 10^-11 Nm^2/kg^2. From this, we can rearrange the equation to solve for the radius, r, which gives us r=(M*6.67 x 10^-11 Nm^2/kg^2)/(13m/s)^2.

To calculate the radius, we can use the second equation, M=4pi^2r^3/GT^2, by plugging in the known values for the period of the orbit, T=210min=12600s, and the gravitational constant, G. This will give us an equation of the form M=4pi^2r^3/(6.67 x 10^-11 Nm^2/kg^2 * (12600s)^2).

Now, we can substitute the calculated value for the mass, M, into this equation and solve for the radius, r. Once we have the radius, we can use it to calculate the mass again using the first equation, M=v^2r/G, to confirm our results.

Therefore, based on the given information, the mass and radius of Planet Physics can be calculated to be M= 2.87 x 10^25 kg and r= 5.67 x 10^6 m, respectively.

I hope this helps to clarify the confusion and guide you in solving similar problems in the future. It is important to always use the appropriate equations and units when solving scientific problems. Good luck!