Answer: 43.51 m/s.
Step-by-step explanation:
AI-generated answer
To determine how long the feather remained in the air, we can use the kinematic equation for vertical motion:
Δy = v₀t + (1/2)gt²
Where:
- Δy is the vertical displacement (in this case, the height of the drop)
- v₀ is the initial velocity (which is zero, since the feather is dropped)
- t is the time
- g is the acceleration due to gravity (approximately 9.8 m/s²)
In this case, the vertical displacement (Δy) is 97.0m and the initial velocity (v₀) is 0 m/s. Plugging these values into the equation, we can solve for t:
97.0 = 0 * t + (1/2) * 9.8 * t²
Rearranging the equation, we get:
4.9t² = 97.0
Dividing both sides by 4.9, we have:
t² = 97.0 / 4.9
Simplifying further:
t² = 19.8
Taking the square root of both sides, we find:
t ≈ √19.8
t ≈ 4.45 seconds
Therefore, the feather remained in the air for approximately 4.45 seconds.
To determine the feather's speed just before striking the ground, we can use another kinematic equation for vertical motion:
v = v₀ + gt
Where:
- v is the final velocity (which is what we want to find)
- v₀ is the initial velocity (which is still zero, since the feather is dropped)
- t is the time
- g is the acceleration due to gravity (approximately 9.8 m/s²)
Since we already found that the time (t) is approximately 4.45 seconds, we can plug that into the equation:
v = 0 + 9.8 * 4.45
v ≈ 43.51 m/s
Therefore, the feather's speed just before striking the ground is approximately 43.51 m/s