91Ó°ÊÓ

Free fall motion describes the movement of an object solely under the influence of gravity. This means no other forces, like air resistance, act on the object. In our exercise, the key is in free fall. This means it accelerates downward at the same rate as the acceleration due to gravity, which is approximately 9.8 meters per second squared (m/s²).
Understanding free fall is crucial in physics because it's an ideal motion state where only gravitational force affects the object. It allows us to predict how long it takes for an object to fall from a specific height using the equation:\[ h = \frac{1}{2}gt^2 \]Here, \( h \) is the height, and \( t \) is the time in seconds. You rearrange this equation to solve for \( t \) using:\[ t = \sqrt{\frac{2h}{g}} \]Plugging in the height of 45 meters, this formula helps determine that the key will take approximately 3.03 seconds to fall to the water.

Kinematics is the branch of physics that studies the motion of objects without considering the forces that cause the motion. It focuses on describing movement with quantities such as displacement, velocity, and acceleration.

In our problem, we applied a basic kinematic equation to determine the time taken for an object to fall. By understanding kinematic principles, we can predict how fast an object moves or how long it stays in motion by knowing some key variables.

• Displacement: Refers to how far an object is from the starting point, regardless of the path.
• Velocity: The rate of change of displacement, a vector quantity, meaning it has direction.
• Acceleration: The rate at which velocity changes, which in free fall, is constant at approximately 9.8 m/s².

This understanding allows us to calculate the exact timing of events, like when the key hits the boat, using fundamental equations and given initial conditions.

Constant velocity motion refers to movement at a steady speed in a straight line. The boat in our exercise is an example of this concept. It was described to be moving with constant velocity, meaning it does not speed up or slow down.
Here's what you need to consider about constant velocity motion:

• Constant Speed: The speed remains unchanged over time.
• Unchanging Direction: The movement direction is fixed, making it a straight-line motion.

The main formula used for constant velocity is:\[ v = \frac{d}{t} \]In the exercise, the boat traveled 12 meters while the key took about 3.03 seconds to fall. By placing these values into the formula, we find out the boat's speed is approximately 3.96 m/s. It's critical to grasping these basics to solve problems where objects must meet or intercept in motion.