Snowball on ice. You and your son is throwing snow balls at each other on a slippery (frictionless) frozen lake. Your mass is \(80 \mathrm{~kg}\) and his mass is \(20 \mathrm{~kg}\), and you both start at rest. You throw a big snow ball \((2 \mathrm{~kg})\) towards your son. The snow ball has an initial speed of \(20 \mathrm{~m} / \mathrm{s}\) and you throw it at an angle of \(30^{\circ}\) with the horizon. (a) What is the momentum of the snow ball? (b) What are you and your sons velocities after you have thrown the snow ball, but before the snow ball reaches him? (c) Your son catches the snow ball. What are your and your sons velocities now?

In physics, the principle of conservation of momentum is a key concept. It states that the total momentum of a closed system is constant if no external forces act on it. In simpler terms, momentum before an event equals the momentum after an event.
In practice, this means if you and your son start throwing snowballs on a frictionless lake, the total momentum remains zero since it was zero initially. This principle helps us calculate velocities after actions like throwing or catching a snowball.
The formula we use is \(\text{momentum}_{\text{initial}} = \text{momentum}_{\text{final}}\), where momentum is the product of mass and velocity. This becomes very useful in problems where objects interact but are isolated from external forces.

When an object is thrown at an angle, its velocity has both horizontal and vertical components. To solve mechanics problems effectively, you must separate these components.
For a snowball thrown at an angle of 30° with a velocity of 20 m/s, we use trigonometry to find the horizontal component. This is done using the formula \(\text{v}_{\text{horizontal}} = v \cdot \cos(\theta)\)
Horizontal Component: \(\text{v}_{\text{horizontal}} = 20 \cdot \cos(30°) = 20 \cdot \frac{\sqrt{3}}{2} = 10\sqrt{3}\) m/s
The vertical component would be \(\text{v}_{\text{vertical}} = 20 \cdot \sin(30°)\). Though in this problem, the vertical component isn't needed. Understanding both components is essential for solving a wide range of mechanics problems.

A frictionless surface is ideal for understanding basic mechanics because it eliminates the effects of friction. This means the only forces acting are those we apply directly.
When you and your son throw snowballs on a frozen lake, the lack of friction means that there are no additional horizontal forces to consider. This simplification helps us focus on momentum conservation.

• There are no resistive forces to slow down the motion horizontally.
• Velocities and momentum can be calculated without factoring in frictional losses.

In practical scenarios, frictionless conditions are rare, but they help illustrate fundamental physics principles clearly, making it easier to understand the underlying mechanics.