Pam, wearing a rocket pack, stands on frictionless ice. She has a mass of 44 kg. The rocket supplies a constant force for 22.0 m, and Pam acquires a speed of 62.5 m/s. Assume that air resistance is negligible.

(a) What is the magnitude of the force?

To find the magnitude of the force, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration. In this case, the force is supplied by the rocket pack, causing Pam to accelerate.

First, we need to calculate the acceleration of Pam using the formula:

a = (v - u) / t

Where:
a = acceleration
v = final velocity
u = initial velocity
t = time

In this case, Pam starts from rest (initial velocity, u = 0) and acquires a speed of 62.5 m/s (final velocity, v), over a distance of 22.0 m. Therefore:

a = (62.5 m/s - 0 m/s) / (22.0 m)
a = 62.5 m/s / 22.0 m
a ≈ 2.84 m/s²

Now, we can substitute the values into Newton's second law to find the force:

F = m * a

Where:
F = force
m = mass
a = acceleration

Given:
m = 44 kg
a = 2.84 m/s²

F = 44 kg * 2.84 m/s²
F ≈ 125.12 N

Therefore, the magnitude of the force exerted by the rocket pack is approximately 125.12 N.

To calculate the magnitude of the force applied by the rocket pack, we can use Newton's Second Law of Motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, we can consider the change in velocity (Δv) as acceleration, as there is no time specified.

The equation can be written as:
F = m * Δv

Given:
m (mass) = 44 kg
Δv (change in velocity) = 62.5 m/s

Substituting the values into the equation, we have:
F = 44 kg * 62.5 m/s

Simplifying the equation gives us:
F = 2750 kg·m/s

Therefore, the magnitude of the force applied by the rocket pack is 2750 kg·m/s.

Force x distance = change in kinetic energy

Force = (1/2) M V^2/(22 meters)
= (1/2)*44*(62.5)^2/22 = ___ Newtons