Question

a student drops a feather off the top a building. the feather averages 1.5 m/s while fluttering to the ground. determine all unknowns.
s_i = 0 m/s
s = 1.5 m/s
s_f = 0.5 m/s

Explanation:

Step1: Identify initial velocity

The feather is dropped, so initial velocity \( s_i = 0 \, \text{m/s} \).

Step2: Identify average velocity

Given average velocity \( \bar{s} = 1.5 \, \text{m/s} \).

Step3: Calculate final velocity

For motion with constant acceleration (near - Earth, acceleration due to gravity, but here we use the formula for average velocity: \( \bar{s}=\frac{s_i + s_f}{2} \).
We know \( s_i = 0 \) and \( \bar{s}=1.5 \).
Substitute into the formula: \( 1.5=\frac{0 + s_f}{2} \).
Multiply both sides by 2: \( s_f=2\times1.5 = 3 \, \text{m/s} \). Wait, but the yellow box has 0.5, maybe there is a mis - understanding. Wait, maybe the problem is about something else. Wait, if we assume that maybe it's a different approach. Wait, no, the standard formula for average velocity when acceleration is constant (like free fall, but feather has air resistance, but maybe in the problem's context, we use \( \bar{v}=\frac{v_i + v_f}{2} \).
If \( v_i = 0 \), \( \bar{v}=1.5 \), then \( v_f = 2\bar{v}-v_i=2\times1.5 - 0 = 3 \, \text{m/s} \). But the yellow box has 0.5, maybe the problem has a typo or I misread. Wait, maybe the variables are different. Wait, the problem says "determine all unknowns". Let's re - check. The initial velocity \( s_i = 0 \) (dropped), average velocity \( \bar{s}=1.5 \). If we use \( \bar{s}=\frac{s_i + s_f}{2} \), then \( s_f = 2\bar{s}-s_i=2\times1.5 - 0 = 3 \, \text{m/s} \). But the yellow box in the image has 0.5, maybe that's an error. But according to the formula, the final velocity should be 3 m/s.

Answer:

If we use the average velocity formula \( \bar{s}=\frac{s_i + s_f}{2} \) with \( s_i = 0 \, \text{m/s} \) and \( \bar{s}=1.5 \, \text{m/s} \), then \( s_f=3 \, \text{m/s} \). (Note: There might be a discrepancy with the yellow box value in the image, possibly due to a problem error or mis - interpretation of variables.)