A peregrine falcon dives at a pigeon. The falcon starts downward from rest with free-fall acceleration. If the pigeon is 66.0 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
h=gt²/2 =>
t =sqrt(2h/g)=
=sqrt(2•66/9.8) =3.67 s
To find the time it takes for the falcon to reach the pigeon, we can use the equations of motion for an object accelerating due to gravity.
1. First, we need to determine the time it takes for the falcon to cover the distance of 66.0 m.
We can use the equation:
d = (1/2) * g * t^2
where:
- d is the distance (66.0 m in this case)
- g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth)
- t is the time we want to find
Rearranging the equation to solve for t, we have:
t^2 = (2 * d) / g
t = sqrt((2 * d) / g)
t = sqrt((2 * 66.0 m) / 9.8 m/s^2)
t ≈ sqrt(13.47 s^2)
t ≈ 3.67 s (rounded to two decimal places)
Therefore, it takes approximately 3.67 seconds for the falcon to reach the pigeon.