Cannon shot on airless planet with x gravity

[Mugen112]

I've been struggling with this problem for over two hours...PLEASE HELP!

Homework Statement

A huge cannon is assembled on an airless planet. The planet has a radius of 5.0 \times 10^{6}\;{\rm m} and a mass of 2.6 \times 10^{24}\;{\rm kg}. The cannon fires a projectile straight up at 3800 m/s.

An observation satellite orbits the planet at a height of 700 km. What is the projectile's speed as it passes the satellite?

Homework Equations

1/2mv₂² - GMm/r+y₂ = 1/2mv₁²- GMm/R

The Attempt at a Solution

I'm trying to use that equation and solve for y₂. I keep coming up with a negative number.

v₂= sqroot[v₁² - (2GM/R) - (2GM/R+y₂)]

you can see that when u subtract, you will get a negative under the root... I am going to go crazy. any help is appriciated.

 

[alphysicist]

Hi Mugen112,

I've been struggling with this problem for over two hours...PLEASE HELP!

Homework Statement

A huge cannon is assembled on an airless planet. The planet has a radius of 5.0 \times 10^{6}\;{\rm m} and a mass of 2.6 \times 10^{24}\;{\rm kg}. The cannon fires a projectile straight up at 3800 m/s.

An observation satellite orbits the planet at a height of 700 km. What is the projectile's speed as it passes the satellite?

Homework Equations

1/2mv₂² - GMm/r+y₂ = 1/2mv₁²- GMm/R

The Attempt at a Solution

I'm trying to use that equation and solve for y₂. I keep coming up with a negative number.

v₂= sqroot[v₁² - (2GM/R) - (2GM/R+y₂)]

I don't believe this equation is correct. When you moved the potential energy term from the left side to the right its sign should have become positive.

you can see that when u subtract, you will get a negative under the root... I am going to go crazy. any help is appriciated.