A bullet is shot into a metal plate and comes to a stop. It experiences an impulse I. An identical bullet travelling at the same speed is shot into thick layers of cloth and comes to a stop. How does the second bullets impulse compare to the first?

the second bullet and the first bullet will both have equal amount of impulse m(V - u) = m(0 - u) = -mu

Explanation: impulse is the change of momentum or the products of force and time.

Ft = m(v-u) = impulse.

Both bullets posses equal amount of force, both bullets will experience equal impulse in coming to rest since they posses equal mass and their initial and final velocities are u and V respectively.

V = 0 sinice they both come to rest.

Ft = m(0 - u) = -mu,

The -ve sign indicates it is towards the direction opposite the direction of motion.

The bullet that penetrates the plate will come to rest faster compared to the bullet that penetrates the layer of clothes.

This means the bullet that penetrates the cloth spends a longer time before coming to rest and hence meets a lesser resistant force compared to the bullet that penetrates the block.

One equation that gives us information about how a satellite moves around an object is the following one:

v^2 = (G*M)/R

Where V is the velocity of the satellite, G is the gravitational constant, M is the mass of the Earth in this case, and R is the distance between the satellite and the Earth.

If you double M, there are a range of probabilities, where the extremes are:

The velocity of the moon does not change:

In this situation we have:

v^2 = (G*2M)/R'

where R' is the new distance, if we want to restore the previous equation, here we must have R' = 2R, this means that the distance between the Earth and the moon is also doubled.

The other extreme is that the distance is not changed:

(v')^2 = (G*2M)/R = 2*v^2

where v' is the new velocity  

Then we have that v' = √2*v will be the new velocity of the moon.

And there are the possibilities where both velocity and distance changes, which are a lot more.