Final answer:
It takes about 1.51 seconds for the fish's vertical speed to double from the moment it is dropped by the eagle flying at 7.4 m/s.
Step-by-step explanation:
To determine how much time passes before the fish's speed doubles after being dropped by an eagle flying horizontally at 7.4 m/s, we need to consider the vertical component of the motions separately from the horizontal motion since the two are independent of each other.
Upon release, the fish has an initial vertical speed of 0 m/s because it's only moving horizontally. As the fish falls, it accelerates due to gravity (approximately 9.81 m/s2 on Earth). The fish's vertical speed will double to 14.8 m/s (since 7.4 m/s is the initial horizontal speed). We can use the equation for uniform acceleration,
v = u + at,
where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity, and t is the time. Substituting the known values and solving for t gives us:
14.8 m/s = 0 m/s + (9.81 m/s2)t,
t ≈ 1.51 seconds.
So, it takes approximately 1.51 seconds for the fish's vertical speed to double from when it was dropped by the eagle.