State the principle of conservation of linear momentum and apply it to a system of two boys and a trolley.

$\boxed{\text{}The total linear momentum of an isolated system remains constant in both magnitude and direction.\text{}}$

System: Two boys + trolley.
Initial state: Trolley and boys are at rest.
Mass of each boy = $m$
Total mass of boys $m_{boys} = 2m$
Mass of trolley $m_{trolley} = 4m$
Initial velocity of boys $u_{boys} = 0 \text{ m/s}$
Initial velocity of trolley $u_{trolley} = 0 \text{ m/s}$
Final velocity of boys $v_{boys} = 2 \text{ m/s}$ (Let's take this direction as positive)
Final velocity of trolley $v_{trolley} = ?$

2015 Limpopo Prelim Paper 1 Q5

Mathematically, Impulse ($F\Delta t$) = Change in momentum ($\Delta p = m\Delta v$).

Reason: The system (soccer ball + player's head) is not an isolated system because there is an external force acting on it from the player's body (connected to the ground).

Mass of ball $m = 0.5 \text{ kg}$
Initial velocity of ball $u = 6 \text{ m/s}$ (Let's take the initial direction as positive)
Final velocity of ball $v = -9 \text{ m/s}$ (headed directly back, so opposite direction)
Time of contact $\Delta t = 0.02 \text{ s}$
Average force $F = ?$

Reason: A non-compressible ball will experience the same change in momentum ($\Delta p$) but over a shorter contact time ($\Delta t$) because it deforms less. Since $F = \frac{\Delta p}{\Delta t}$, a smaller $\Delta t$ for the same $\Delta p$ results in a larger force $F$.