Pam has a mass of 44.0 kg and she is at rest on smooth, level, frictionless ice. Pam straps on a rocket pack. The rocket supplies a constant force for 22.0 m and Pam acquires a speed of 58.0 m/s.

To solve this problem, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the force is applied by the rocket pack, and we need to find the acceleration Pam experienced.

The equation that relates force, mass, and acceleration is:

F = m * a

Where:
F = Force applied by the rocket pack
m = Mass of Pam
a = Acceleration of Pam

Given:
m = 44.0 kg (mass of Pam)
F = ? (force applied by the rocket pack)

We can rearrange the formula to solve for force:

F = m * a

Now, we need to find Pam's acceleration. We can use the equation:

v^2 = u^2 + 2as

Where:
v = final velocity (58.0 m/s)
u = initial velocity (0 m/s, because Pam is at rest)
a = acceleration
s = displacement (22.0 m)

Rearranging the equation to solve for acceleration, we get:

a = (v^2 - u^2) / (2s)

Substituting the given values:

a = (58.0^2 - 0^2) / (2 * 22.0)

a = 2036.0 / 44.0

a = 46.27 m/s^2

Now that we have the acceleration, we can find the force applied by the rocket pack using the equation:

F = m * a

Substituting the given values:

F = 44.0 * 46.27

F = 2034.68 N

Therefore, the force applied by the rocket pack is approximately 2034.68 Newtons.