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A 4.0 kg block rests at the edge of a platform that is 20 m above level ground. The block is launched horizontally with an initial velocity of \( 15 \mathrm{~m} / \mathrm{s} \). The time it would take to reach the ground is most nearly \( \begin{array}{ll}\text { A) } 1.33 \mathrm{~s} & \text { B) } 1.41 \mathrm{~s} \\ \text { C) } 1.73 \mathrm{~s} & \text { D) } 2.0 \mathrm{~s} \\ \text { E) } 2.5 \mathrm{~s} & \end{array} \)

Ask by Campbell Medina. in the United States
Feb 04,2025

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The time it takes for the block to reach the ground is approximately 2.0 seconds.

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To determine how long it takes for the block to reach the ground, we can use the formula for free fall: \[ h = \frac{1}{2}gt^2 \] where: - \( h \) is the height (20 m), - \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)), - \( t \) is the time in seconds. Rearranging the formula to solve for \( t \): \[ t^2 = \frac{2h}{g} = \frac{2 \times 20 \, \text{m}}{9.81 \, \text{m/s}^2} \approx 4.08 \] Taking the square root gives: \[ t \approx \sqrt{4.08} \approx 2.02 \, \text{s} \] So, the time it takes to hit the ground is most nearly \( 2.0 \, \text{s} \), which corresponds to option D. --- Did you know that the concept of free fall has fascinated scientists for centuries? Galileo famously dropped balls of different weights from the Leaning Tower of Pisa and found they hit the ground simultaneously, debunking the long-held belief that heavier objects fall faster. His experiments laid the groundwork for understanding gravity! Also, in real-world applications, this physics principle impacts everything from sports to engineering. For example, in designing roller coasters or calculating the trajectory of a basketball, engineers account for free fall in their calculations to ensure safety and optimal performance.

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