The velocity of the eagle is 7.0 m/s
Explanation:
The motion of the fish is a projectile motion, which consists of two independent motions:
- A uniform motion (constant velocity) along the horizontal direction, where the horizontal velocity of the fish is equal to the horizontal velocity of the eagle
- An accelerated motion with constant acceleration (acceleration of gravity) in the vertical direction
We start by analyzing the vertical motion, using the following suvat equation:
![s=ut+\frac{1}{2}at^2](https://tex.z-dn.net/?f=s%3Dut%2B%5Cfrac%7B1%7D%7B2%7Dat%5E2)
where:
s = 6.1 m is the vertical displacement of the fish
u = 0 is the initial vertical velocity of the fish
is the acceleration of gravity
t is the time
Solving for t, we find the time of flight of the fish:
![t=\sqrt{\frac{2s}{a}}=\sqrt{\frac{2(6.1)}{9.8}}=1.12 s](https://tex.z-dn.net/?f=t%3D%5Csqrt%7B%5Cfrac%7B2s%7D%7Ba%7D%7D%3D%5Csqrt%7B%5Cfrac%7B2%286.1%29%7D%7B9.8%7D%7D%3D1.12%20s)
Now we know that during this time, the fish travels a horizontal distance of
x = 7.9 m
Therefore, the horizontal velocity of the fish is
![v_x = \frac{x}{t}=\frac{7.9}{1.12}=7.0 m/s](https://tex.z-dn.net/?f=v_x%20%3D%20%5Cfrac%7Bx%7D%7Bt%7D%3D%5Cfrac%7B7.9%7D%7B1.12%7D%3D7.0%20m%2Fs)
And therefore, this is the initial velocity of the eagle.
Learn more about projectile motion:
brainly.com/question/8751410
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