Question

A peregrine falcon dives at a pigeon. The falcon starts with zero downward velocity and falls with the acceleration of gravity. If the pigeon is 76.0 m below the initial height of the falcon, how long does it take the falcon to intercept the pigeon?

Answer 1

Answer:

t = 3.94 s

Explanation:

This can be modeled as a case of free fall motion. Because, the falcon is going down with acceleration, that is equal to acceleration due to gravity. To find the time taken by the falcon to intercept the pigeon, we will use second equation of motion for vertical direction:

$h = v_{i}t + \frac{1}{2}gt^2$

where,

h = height = 76 m

vi = initial speed of falcon = 0 m/s

t = time required = ?

g = acceleration due to gravity = 9.81 m/s²

Therefore,

$76\ m = (0\ m/s)(t) + \frac{1}{2}(9.81\ m/s^2)t^2\\t^2 = \frac{(2)(76\ m)}{9.8\ m/s^2}\\\\t = \sqrt{ 15.49\ s^2}$

t = 3.94 s