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

Answer 2

The kinematics allows to find the result for the time it takes the falcon to reach the pigeon is:

• Time is t = 3.94 s

Kinematics studies the motion of bodies looking for relationships between position, velocity and acceleration.

A reference system is a coordinate system with respect to which to carry out the measurements. In the attachment we set a reference system in the pigeon with the vertical direction upwards as positive.

They indicate that the height of the hawk is I = 76 m and its initial vertical velocity is zero.

            y = y₀ + v₀ t - ½ g t²

            0 = y₀ - ½ g t²

            $t = \sqrt{\frac{2y_o}{g} }$

Let's calculate.

          $t = \sqrt{\frac{2 \ 76.0}{9.80} }$  

          t = 3.94 s

In conclusion using kinematics we can find the result for the time it takes the falcon to reach the pigeon is:

• Time is t = 3.94 s

Learn more about kinematics here:  brainly.com/question/24760588