An eagle is flying horizontally at a speed of 4.6 m/s when the fish in her talons wiggles loose and falls into the lake 4.2 m below. Calculate the vertical component of the velocity of the fish relative to the water when it hits the water.

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Answer:

v = 9.07 m/s

the vertical component of the velocity of the fish relative to the water when it hits the water is 9.07 m/s

Explanation:

Given;

An eagle is flying horizontally at a speed of 4.6 m/s

Initial horizontal velocity uh = 4.6 m/s

Initial vertical velocity uy = 0

Height to fall d = 4.2 m

Acceleration due to gravity g = 9.8 m/s^2

The final vertical velocity of the fish when it hits the water can be calculated using the equation of motion;

v^2 = u^2 + 2as

v^2 = uy^2 + 2gd

uy = 0

v^2 = 2gd

v = √(2gd)

Substituting the given values;

v = √(2×9.8×4.2)

v = 9.073036977771 m/s

v = 9.07 m/s

the vertical component of the velocity of the fish relative to the water when it hits the water is 9.07 m/s