Question

a student drops a feather from a height of 26.0m. determine all unknowns and answer the following questions. how long did the feather remain in the air? what was the feathers speed just before striking the ground?

Explanation:

Step1: Use free - fall displacement formula

The displacement formula for free - fall motion is $h = v_0t+\frac{1}{2}gt^2$. Since the feather is dropped ($v_0 = 0$), the formula simplifies to $h=\frac{1}{2}gt^2$. We know $h = 26.0m$ and $g = 9.8m/s^2$. Rearranging for $t$, we get $t=\sqrt{\frac{2h}{g}}$.
$t=\sqrt{\frac{2\times26.0}{9.8}}\approx\sqrt{\frac{52}{9.8}}\approx\sqrt{5.306}\approx2.30s$

Step2: Use free - fall velocity formula

The velocity formula for free - fall motion is $v = v_0+gt$. Since $v_0 = 0$, the formula is $v = gt$. Substituting $g = 9.8m/s^2$ and $t\approx2.30s$, we get $v=9.8\times2.30 = 22.54m/s$

Answer:

How long did the feather remain in the air? 2.30 s
What was the feather's speed just before striking the ground? 22.54 m/s