Question

An eagle is flying horizontally at a speed of 3m/s when the fish in her talons wiggles loose and falls into the lake 10m below. Calculate the velocity of the fish relative to the water when it hits the water.

Answer 1

Velocity of the fish relative to the water when it hits the water = 14.32 m/s along 77.91° below horizontal.

Step-by-step explanation:

Vertical motion of fish:

Initial speed, u = 0

Acceleration, a = 9.81 m/s²

Displacement, s = 10 m

We have equation of motion, v² = u² + 2as

Substituting

v² = 0² + 2 x 9.81 x 10 = 196.2

v = 14 m/s

Final vertical speed = 14 m/s

Final horizontal speed = initial horizontal speed = 3 m/s

Final velocity = 3 i - 14 j m/s

Magnitude

`v=√(3^2+(-14)^2)=14.32m/s`

Direction

`\theta =tan^(-1)\left ( (-14)/(3)\right )=-77.91^0`

Velocity of the fish relative to the water when it hits the water = 14.32 m/s along 77.91° below horizontal.