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Free fall occurs when an object is moving under the sole influence of gravity. This means that no other forces, like air resistance, are acting on the object. In the case of the water balloon, because we've ignored air resistance, its motion can be considered as free fall.

When an object is in free fall, it accelerates downward due to gravity at a constant rate. We can use kinematic equations to determine the velocity, position, and time for such motion. An important thing to remember is that, irrespective of the initial velocity, once in free fall, only gravity is influencing the speed.

Gravitational acceleration ( g ) is the rate at which an object speeds up as it falls freely to the ground. On Earth, this acceleration is approximately 9.81 meters per second squared (m/s²). It's important to remember this value because it's a key factor in calculating many properties of motion, such as velocity and distance fallen.

In our water balloon example, gravitational acceleration causes the balloon to accelerate as it falls. Even though it started with an initial downward velocity of 6.00 m/s, the constant pull of gravity will increase its speed steadily. This means that every second, its speed increases by 9.81 m/s due to gravity alone.

Kinematic equations are a set of formulas used to describe the motion of objects when they move with uniform acceleration. These equations relate the five fundamental variables: initial velocity ( v_0 ), final velocity ( v ), acceleration ( a ), time ( t ), and displacement ( y ).

Here's a quick rundown of the most used kinematic equations:

• Velocity: \( v = v_0 + at \)
• Displacement: \( y = v_0t + \frac{1}{2}at^2 \)
• Velocity squared: \( v^2 = v_0^2 + 2ay \)

In the water balloon scenario, these equations help calculate the balloon's velocity and distance fallen over time. Starting with initial conditions, you can plug values into these equations to find the desired information about the object's motion.

Uniform acceleration refers to a constant change in velocity per unit of time. In simpler terms, if an object experiences uniform acceleration, its speed will increase or decrease at a steady rate.

A prime example is the acceleration due to gravity, which stays unchanged at 9.81 m/s² for any object in free fall. This constant acceleration is what makes the calculation of falling objects predictable using kinematic equations.

In our exercise, the water balloon thrown downward initially means it starts with some speed. The addition of uniform gravitational acceleration causes a linear increase in its velocity over time, making it relatively straightforward to analyze its motion.