The minimum height of the dive needed to achieve the given speed is v = 69 m/s is 242.9 m.
Given information:
The mass of peregrine falcon is, m = 480
The final speed reached by the peregrine falcon in a vertical dive is, v = 69 m/s
It is given that the falcon is diving vertically downward. It can be compared with the same situation as the free-falling object under the effect of gravity only. So, the initial velocity of the falcon will be u = 0 m/s as the motion starts with rest.
The value of the gravitational acceleration of gravity is, g = 9.80 m/s²
Now, using the third equation of motion, the minimum height required for the final speed will be,
v² - u² = 2gh
69² - 0² = 2 × 9.8 × h
h = 242.9m.
Therefore, the minimum height of the dive needed to achieve the given speed is 242.9 m.
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