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Free fall is when an object moves only under the influence of gravitational force. There are no other forces acting on it, which means that the motion is completely vertical. In the case of our golf ball, once it leaves the cliff, it is in free fall.

• The initial vertical speed is 0 m/s because the ball starts falling horizontally.
• The gravitational acceleration, denoted as \( g \), is 9.81 m/s².

In free fall, the vertical distance fallen \( s \) can be calculated using the equation: \[ s = ut + \frac{1}{2}gt^2 \]Here, \( s \) is the distance fallen, \( u \) is the initial vertical speed (0 m/s for free fall), \( g \) is gravitational acceleration, and \( t \) is time. Since it is rolling off horizontally, our focus is on the gravity pulling it down, thus making the calculations simple yet effective for finding the time of descent.

Projectile motion involves both horizontal and vertical components, yet they operate independently. This is a critical understanding in physics problems, allowing one to solve for one dimension without influencing the other.

• Horizontal motion: The object maintains a constant speed, given at 11.4 m/s here, because there is no force causing horizontal acceleration.
• Vertical motion: Governed by free fall, starts from rest in terms of speed and is influenced only by gravity.

Even though these components are independent, they occur simultaneously. To calculate how long the ball is in the air, you use vertical motion equations. To find how far it travels horizontally, you use the time of flight and horizontal speed.

Determining the resulting speed just before an impact or at any given point involves combining horizontal and vertical speed components.

• Vertical speed is computed using: \[ v_y = u + gt \] Where \( u \) is the initial vertical speed (0 m/s here) and \( t \) is the time spent falling.
• The horizontal speed remains constant at 11.4 m/s.

The combined speed, or the velocity just before the object strikes, is found by applying the Pythagorean theorem:\[ v = \sqrt{v_x^2 + v_y^2} \]Where \( v_x \) is the horizontal speed and \( v_y \) is the vertical speed just before impact. Understanding this helps in visualizing how speed vectors work to combine different motion directional speeds into a unified measure.

Physics equations describe how objects move, offering a blueprint for solving motion problems. In projectile motion, several key physics equations are used to unravel the problem.

• The equation \( s = ut + \frac{1}{2}gt^2 \) applies to vertical motion, allowing you to calculate the time in the air and understand how gravity acts over time.
• For horizontal motion, the formula \( x = vt \) isn't necessary to find the flight's duration but helps determine horizontal displacement.
• Velocity computation is unified through: \[ v = \sqrt{v_x^2 + v_y^2} \]This shows how different components of speed come together for a full picture of motion.

These equations empower you to split complex motion into simpler, more manageable parts, ultimately leading toward solutions comprehensively tied to forces and movement principles.