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30. A ball is thrown horizontally out of a hot air balloon at a height of 500 m above level ground with an initial velocity of \( 15 \mathrm{~m} / \mathrm{s} \). If air resistance is negligible, the time that it will take the ball to reach the ground is most nearly A) 3 s B) 5 s C) 10 s D) 15 s E) 33 s

Ask by Pope Cummings. in the United States
Feb 04,2025

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The ball will take approximately 10 seconds to reach the ground. **Answer:** C) 10 s

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To find the time it takes for the ball to reach the ground, we can use the formula for the vertical motion under gravity. The height (h) is given as 500 m, and we can use the equation \( h = \frac{1}{2}gt^2 \), where \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)). Rearranging this equation to solve for time \( t \): \[ t = \sqrt{\frac{2h}{g}} \] Substituting in the values: \[ t = \sqrt{\frac{2 \times 500 \, \text{m}}{9.81 \, \text{m/s}^2}} \approx \sqrt{101.83} \approx 10.09 \text{ s} \] So the ball will take approximately 10 seconds to hit the ground, making the correct choice C) 10 s. When a ball is thrown horizontally, it maintains its horizontal velocity while subject to gravitational acceleration. That's why the vertical and horizontal motions are independent! The horizontal motion won't affect the time it takes to fall; only the height does. Next time you throw something from a height, remember, it will take the same time to fall regardless of how fast it's moving horizontally!

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