Final answer:
To calculate the initial speed of the rock, we use conservation of energy to set up an equation comparing kinetic and potential energy at the start with potential energy at the maximum height. Solving this equation allows us to find the initial speed after calculating the acceleration due to gravity on planet Globus using its given mass and radius.
Step-by-step explanation:
To find the initial speed of the rock as it left the astronaut's hand on the planet Globus, we can use the conservation of energy principle. At the point of release, the rock has kinetic energy due to its speed and potential energy due to its height. When the rock reaches its maximum height, it has maximum potential energy and zero kinetic energy.
The conservation of energy equation can be expressed as:
Kinetic Energy at the start + Potential Energy at the start = Potential Energy at the maximum height
\(\frac{1}{2}mv^2 + mgh = mg(h + 2200)\)
Where m is the mass of the rock, v is the initial speed we want to find, g is the acceleration due to gravity, h is the initial height which we can take as 0 since we ignore the astronaut's height, and 2200 m is the maximum height above the planet's surface.
We cancel out m and solve for v:
\(\frac{1}{2}v^2 = g(2200)\)
Finally, using the formula for gravity g = G \times \frac{{M}}{{r^2}}, where G is the gravitational constant, M is the mass of Globus (7.1\( \times \)10\(^{18}\) kg), and r is the radius of Globus (65,000 m), we calculate g for Globus and find v.