A480 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?

elevation = 243[m]

Explanation:

This problem can be solved using the principle of energy conservation, where potential energy becomes kinetic energy. At the point where the speed is equal to 69 [m / s] will be taken as the reference point for potential energy, at this point all potential energy will have been transformed into kinetic energy.

So this kinetic energy will be equal to the potential energy at the beginning.

The falcon was originally at 243 [m] above the point (reference point) where he reached the speed given.

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft