The Correct Answer and Explanation is:
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9) Step 5: Determine the egg’s altitude at 15 seconds.
This instruction is a component of a larger problem, likely from a physics or mathematics course focusing on kinematics, which is the study of motion. The phrase “Step 5” implies that previous steps have already been completed, which would have established the necessary context and initial conditions for this calculation. The core task is to find the vertical position, or height, of an egg at a specific moment in time, 15 seconds into its flight.
To solve such a problem, a mathematical equation describing the egg’s altitude over time is required. This is known as a position function, often written as h(t), where h represents height and t represents time. For an object moving vertically under the influence of Earth’s gravity, this function is typically a quadratic equation: h(t) = -0.5gt² + v₀t + h₀.
Let’s break down the components of this formula. The term ‘g’ is the constant for acceleration due to gravity, which is approximately 9.8 m/s² or 32 ft/s², with the negative sign indicating a downward pull. The term ‘v₀’ represents the initial velocity, which is the speed and direction the egg was moving at the very start (t=0). For instance, if the egg was thrown upwards, v₀ would be positive; if dropped, v₀ would be zero. Finally, ‘h₀’ is the initial altitude, or the starting height from which the egg was released.
The information needed to define this specific equation, such as the initial velocity and initial height, would have been provided or calculated in the earlier steps of the problem. To complete Step 5, you would substitute the value of 15 for ‘t’ into the established height function. The result of this calculation would yield the egg’s precise altitude at the 15-second mark, providing a snapshot of its position along its trajectory.
