A person standing on ice throws a bowling ball and recoils from this interaction.
The speed of the person's recoil is small because the...

Because the mass of the person is larger

Explanation:

Since there are no external forces acting on the person+bowling ball system, the total momentum of the system is conserved.

The total momentum of the system before the bowling ball is thrown is zero, as they are both at rest:

While the total momentum after the ball has been thrown is:

where

m is the mass of the ball

v is the velocity of the ball

M is the mass of the person

V is the recoil velocity of the person

Since the total momentum is conserved, we can write

So

Which can be re-arranged as

We see that the ratio is very small since the mass of the ball is much smaller than the mass of the person: therefore, V will be much lower than v, so the recoil velocity of the person is much lower than the velocity of the ball.