A peregrine falcon dives at a pigeon. The falcon starts downward from rest with free-fall acceleration. If the pigeon is 53.0 m below the initial position of the falcon, how long does the falcon take to reach the pigeon? Assume that the pigeon remains at rest.
Well, how long does it take to fall 53 meters?
53 = (1/2)(9.81) t^2
t = 3.3 seconds
To find the time it takes for the falcon to reach the pigeon, we can use the equations of motion for free-fall. The key equation to use in this case is:
Δy = (1/2) * g * t^2
where Δy is the vertical displacement, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.
In this problem, the falcon starts from rest, so its initial velocity (vi) is 0 m/s. Additionally, the pigeon remains at rest, so its final velocity (vf) is also 0 m/s.
Given that the vertical displacement (Δy) is 53.0 m, we can rearrange the equation to solve for time:
Δy = (1/2) * g * t^2
53.0 = (1/2) * 9.8 * t^2
Now, we can solve for t:
t^2 = (2 * 53.0) / 9.8
t^2 ≈ 10.897
t ≈ √10.897
t ≈ 3.3 seconds
Therefore, it takes approximately 3.3 seconds for the falcon to reach the pigeon.