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Understanding kinematics in two dimensions is essential for analysing movements like a toy rocket being propelled in the air. In two-dimensional motion, objects have two independent movements: along the horizontal axis (x-axis) and vertical axis (y-axis). These movements are described by separate sets of equations that consider velocity, acceleration, and displacement.

In the case of the toy rocket problem, we deal with the rocket moving horizontally off the building with an initial velocity and an additional horizontal acceleration due to the engine thrust. Vertically, it begins without initial velocity but experiences the constant acceleration due to gravity. To solve such problems, we separately analyze the motion along each axis and then combine the results to determine the resultant path or final position.

Free fall acceleration, typically represented by the symbol \(g\), is the constant acceleration experienced by an object when it is falling solely under the influence of gravity. The value of \(g\) approximates to \(9.81 \text{m/s}^2\) on Earth's surface. Free fall acceleration acts in the downward vertical direction and is a critical factor in determining the time and impact velocity of falling objects.

For the toy rocket scenario, once it leaves the initial thrust of its propulsion, it will accelerate downwards at this rate. It's important to note that the toy rocket's horizontal motion is unaffected by gravity and we consider it only for its vertical motion.

The equations of motion let us predict future motion based on current and past motion conditions. For constant acceleration, they can be written as:

• \( v = v_0 + a t \)
• \( d = v_0 t + \frac{1}{2} a t^2 \)
• \( v^2 = v_0^2 + 2 a d \)

where \(v\) is the final velocity, \(v_0\) is the initial velocity, \(a\) is the acceleration, \(t\) is the time, and \(d\) is the displacement.

For instance, while the horizontal motion of our toy rocket includes an accelerating force from the engine, leading to a variable acceleration, the vertical motion is subject to a consistent acceleration due to gravity. Therefore, we use the appropriate motion equations for each dimension when solving for the time of flight and the horizontal distance traveled.

The term 'time of flight' refers to the duration an object stays in the air. Determining the time of flight for projectile motion is a two-step process: first, we find the time it takes for the object to reach the peak of its trajectory, and second, we find the time it takes to fall back down to its original elevation or to the ground if it starts from a height. However, if an object launches horizontally from a height, like our toy rocket, we only need to consider the descent.

To find the time of flight for our horizontally launched rocket, we can ignore the horizontal motion and just consider the vertical fall. Using the equation \( t = \text{sqrt}{(-2d_y/g)} \), with \( d_y = -30.0 \text{m} \) due to gravity and the height the rocket falls from, allows us to compute how long the rocket will be in the air before it impacts the ground.