Answer:
The radius of the new planet is ~2.04 * 10⁶ m, or 2,041,752 m.
Explanation:
We can use Newton's Law of Universal Gravitation:
Let's look at Newton's 2nd Law:
We can set these equations equal to each other:
The mass of the second mass (astronaut) cancels out. We are left with:
We are solving for the radius of the new planet, so we can rearrange the equation:
Substitute in our known values given in the problem (<u><em>G = 6.67 * 10⁻¹¹ </em></u><em> ; </em><u><em>M = 7.5 * 10²³</em></u><em> ; </em><u><em>a = 12</em></u>).
The radius of the new planet is ~2.04 * 10⁶ m.
1) The mass of the continent is 
2) The kinetic energy of the continent is 1683 J
3) The speed of the jogger must be 6.57 m/s
Explanation:
1)
The continent can be represented as a slab of size

and depth

So its volume is

We also know that the density of the continent is

Therefore, we can calculate its mass as:

2)
The kinetic energy of the continent is given by

where
m is its mass
v is its speed
We have already calculate its mass, while the speed is
v = 3.2 cm/year
We have to convert into SI units first, as follows:

The mass is

So, the kinetic energy of the continent is

3)
Here we have a jogger having the same kinetic energy of the continent, so

And the kinetic energy of the jogger can be expressed as

where
m = 78 kg is the mass of the jogger
v is his speed
We can therefore re-arrange the equation to find the speed of the man, and we get:

Learn more about kinetic energy:
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