A peregrine falcon dives at a pigeon. The falcon starts downward from rest and falls with free-fall acceleration. If the pigeon is 82.8 m below the initial position of the falcon, how long does it take the falcon to reach the pigeon? Assume that the pigeon remains at rest.
To find the time it takes for the falcon to reach the pigeon, we can use the equations of motion for an object in free-fall.
The equation that relates distance, time, and acceleration is:
d = (1/2) * a * t^2
Where:
d is the distance traveled (82.8 m in this case)
a is the acceleration (free-fall acceleration, approximately 9.8 m/s^2)
t is the time
By rearranging the equation, we can solve for time:
t^2 = (2 * d) / a
Substituting the values given, we have:
t^2 = (2 * 82.8 m) / 9.8 m/s^2
t^2 = 16.8979
Taking the square root of both sides, we find:
t ≈ 4.11 s
Therefore, it takes approximately 4.11 seconds for the peregrine falcon to reach the pigeon.