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.
82.8 = 4.9 t^2
t^2 = 16.9
t = 4.1 seconds
To solve this problem, we need to use the kinematic equations of motion for an object falling under free-fall acceleration due to gravity.
The first kinematic equation is:
y = y0 + v0t + (1/2)at^2
where:
y = final position or displacement (82.8 m)
y0 = initial position (0 m, since the falcon starts from rest)
v0 = initial velocity (0 m/s, since the falcon starts from rest)
a = acceleration (-9.8 m/s^2, negative because the falcon is moving downward)
t = time (unknown, what we need to calculate)
Plugging in the given values, the equation becomes:
82.8 = 0 + 0*t + (1/2)(-9.8)*t^2
Simplifying further:
82.8 = -4.9t^2
To solve for t, we rearrange the equation:
t^2 = 82.8 / -4.9
Dividing both sides by -4.9:
t^2 ≈ -16.89796
The time squared is negative, which indicates that there is no real solution for this problem. This means that the falcon and the pigeon will never "meet" in this scenario.
It's important to note that this outcome might not be realistic in a real-world scenario, as there might be other factors at play. However, based on the information provided, the falcon won't reach the pigeon.