QuestionSeptember 4, 2026

A student drops a feather from a height of 77.0m. Determine all unknowns and answer the following questions. How long did the feather remain in the air? square square What was the feather's speed just before striking the ground? square square v

A student drops a feather from a height of 77.0m. Determine all unknowns and answer the following questions. How long did the feather remain in the air? square square What was the feather's speed just before striking the ground? square square v
A student drops a feather from a height of 77.0m. Determine all unknowns and answer the following questions. How long did the feather remain in the air? square square What was the feather's speed just before striking the ground? square square v

Solution
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Answer

Time in air: 3.96 \, \text{s} ### Final velocity: 38.92 \, \text{m/s} Explanation 1. Identify Known Values Initial velocity u = 0 \, \text{m/s}, height h = 77.0 \, \text{m}, acceleration due to gravity g = 9.8 \, \text{m/s}^2. 2. Calculate Time in Air Use the formula for time: **t = \sqrt{\frac{2h}{g}}**. Substitute h = 77.0 \, \text{m} and g = 9.8 \, \text{m/s}^2. 3. Calculate Final Velocity Use the formula for final velocity: **v = \sqrt{2gh}**. Substitute g = 9.8 \, \text{m/s}^2 and h = 77.0 \, \text{m}.

Explanation

1. Identify Known Values<br /> Initial velocity $u = 0 \, \text{m/s}$, height $h = 77.0 \, \text{m}$, acceleration due to gravity $g = 9.8 \, \text{m/s}^2$.<br /><br />2. Calculate Time in Air<br /> Use the formula for time: **$t = \sqrt{\frac{2h}{g}}$**. Substitute $h = 77.0 \, \text{m}$ and $g = 9.8 \, \text{m/s}^2$.<br /><br />3. Calculate Final Velocity<br /> Use the formula for final velocity: **$v = \sqrt{2gh}$**. Substitute $g = 9.8 \, \text{m/s}^2$ and $h = 77.0 \, \text{m}$.
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