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Kinematics is the branch of physics that describes the motion of objects without considering the forces that cause the motion. When solving kinematics problems, we usually find quantities like displacement, velocity, and acceleration using algebraic equations. In the high jump problem, we focused on the vertical motion of the athlete's center of mass.

Kinematic equations are derived from the constant acceleration formulas, where time, displacement, and velocity are related. Given that we know the initial vertical velocity (\(6.00 \text{ m/s}\)) and the acceleration due to gravity (\(9.8 \text{ m/s}^2\)), we can determine how high Dave's center of mass traveled during the jump. This type of motion can be considered as a part of a projectile motion, which we will explain further in the next section.

Projectile motion is a form of motion where an object moves in a curved trajectory under the influence of gravity. It is important to note that the only force acting on the projectile (if we neglect air resistance) is gravity. In our example, the upward journey of the high jumper can be seen as projectile motion.

The jumper's center of mass moves upward and then downward in a symmetrical parabolic path. The highest point of this path is where the velocity component in the vertical direction is zero, which is also the peak of the jump. By calculating the height reached at this peak, we solve an essential part of the projectile motion problem. We treat the motion in the vertical direction separately from the horizontal, applying kinematic equations independently for each direction.

Acceleration due to gravity is the acceleration gained by an object because of the gravitational force of Earth. This acceleration has a standard value of approximately \(9.8 \text{ m/s}^2\) near the Earth's surface and it acts in the downward direction, towards the center of the Earth.

In our high jump problem, gravity plays a significant role in the jumper's motion. It is what accelerates the jumper back down after reaching the peak of the jump. Using the value of the acceleration due to gravity, we can determine the height reached, as seen in the formula \( h = \frac{v^2}{2g} \) where \( h \) is the height, \( v \) is the initial vertical velocity, and \( g \) stands for the acceleration due to gravity. The negative sign is often included to indicate the acceleration is downwards; however, in this formula, we use the magnitude of the values to calculate the height reached.