A 70.5 football player is gliding across very smooth ice at 2.25 . He throws a 0.430 football straight forward.

Incomplete.

To answer your question, I need some clarification. Are you asking for the step-by-step process of what happens when the football player throws the football, or are you asking for another specific piece of information?

To solve this problem, we need to determine the speed of the football after it is thrown. Since it's thrown straight forward, we can assume there is no vertical component to the ball's motion.

The given information is as follows:
Mass of the football player (m1) = 70.5 kg
Initial velocity of the football player (v1) = 2.25 m/s
Mass of the football (m2) = 0.43 kg

Using the principle of conservation of momentum, we can calculate the velocity of the football after it is thrown. The formula for conservation of momentum is:

m1v1 = m2v2

Where:
m1 and m2 are the masses of the football player and the football, respectively,
v1 is the initial velocity of the football player, and
v2 is the final velocity of the football.

Plugging in the given values, we have:

(70.5 kg)(2.25 m/s) = (0.43 kg)(v2)

Now, let's solve for v2 by rearranging the equation:

v2 = (70.5 kg)(2.25 m/s) / (0.43 kg)

Calculating this expression, we get:

v2 ≈ 369.88 m/s

Therefore, the football's velocity after being thrown is approximately 369.88 m/s.