Question

A 480 g peregrine falcon reaches a speed of 69 m/s in a vertical dive called a stoop. If we assume that the falcon speeds up under the influence of gravity only, what is the minimum height of the dive needed to achieve this speed?

Answer 1

Answer:

The minimun height is 242 [m]

Explanation:

We can solve this problem by using the principle of energy conservation, where potential energy becomes kinetic energy. We will take the point where the Falcon reaches the speed of 69 (m/s), as the point where the potential energy is zero, i.e. it will be the reference point.

At the reference point all potential energy has been transformed into kinetic energy, therefore the kinetic energy can be calculated.

$E_{k}=0.5*m*v^{2} \\ where:\\v = velocity = 69 [m/s]\\m = mass = 480[g] = 0.480[kg]\\E_{k} = kinetic energy [J]\\E_{k} =0.5*0.48*(69)^{2} \\E_{k} =1142.64[J]$

Now we can calculate the elevation with respect to the reference point using the definition of the potential energy.

$E_{p}=m*g*h\\ E_{p}=E_{k} \\therefore\\h= E_{p}/(m*g)\\h= 1142.64/(.48*9.81)\\h=242[m]$