Given:
- Mass of the ball (m) = 1 kg
- Initial height (h1) = 20 m
- Final height (h2) = 5 m

To find:
- Magnitude of change in momentum during the collision with the ground

Assumptions:
- We assume that there is no air resistance or any other external forces acting on the ball during its motion.

Explanation:

Step 1: Calculate the initial potential energy:

The initial potential energy (U1) of the ball is given by the formula:

U1 = m * g * h1

where m is the mass of the ball, g is the acceleration due to gravity, and h1 is the initial height.

Substituting the given values, we have:

U1 = 1 kg * 9.8 m/s^2 * 20 m
U1 = 196 J

Step 2: Calculate the final potential energy:

The final potential energy (U2) of the ball is given by the formula:

U2 = m * g * h2

where m is the mass of the ball, g is the acceleration due to gravity, and h2 is the final height.

Substituting the given values, we have:

U2 = 1 kg * 9.8 m/s^2 * 5 m
U2 = 49 J

Step 3: Calculate the change in potential energy:

The change in potential energy (ΔU) is given by the formula:

ΔU = U2 - U1

Substituting the calculated values, we have:

ΔU = 49 J - 196 J
ΔU = -147 J

Step 4: Calculate the change in momentum:

The change in momentum (Δp) is equal to the negative change in potential energy, according to the law of conservation of energy. Thus:

Δp = -ΔU

Substituting the calculated values, we have:

Δp = -( -147 J )
Δp = 147 J

Step 5: Calculate the magnitude of change in momentum:

The magnitude of the change in momentum is given by the absolute value of the change in momentum. Thus:

|Δp| = |147 J|
|Δp| = 147 J

Conclusion:

The magnitude of the change in momentum during the collision with the ground is 147 J.