Question

An eagle is flying horizontally at 6.5 m/s with a fish in its claws. it accidentally drops the fish. how much time passes before the fishes vertical speed matches its horizontal speed?

Answer 1

When the fish is dropped, it falls vertically due to gravity while its horizontal speed remains constant. The time it takes for the fish's vertical speed to match its horizontal speed can be found using the equation Δt = Δv/acceleration, where Δv is the change in velocity in the vertical direction and acceleration is the acceleration due to gravity. By substituting the known values into the equation, we find that it takes approximately 0.6633 seconds for the fish's vertical speed to match its horizontal speed.

Step-by-step explanation:

To find the time it takes for the fish's vertical speed to match its horizontal speed, we can use the kinematic equations and the concept of free fall. When the fish is dropped, it falls vertically due to gravity while its horizontal speed remains constant. The fish will continue to accelerate vertically until its vertical speed matches its horizontal speed. The time it takes for this to happen can be found by using the equation:

Δt = Δv/acceleration

where Δv is the change in velocity in the vertical direction and acceleration is the acceleration due to gravity.

Since the fish was released from rest vertically, its initial vertical speed is 0 m/s. Using the equation Δv = final vertical speed - initial vertical speed, we can determine that Δv is equal to the horizontal speed of the fish, which is 6.5 m/s.

Therefore, substituting the values into the equation, we get:

Δt = 6.5 m/s / 9.8 m/s^2

Solving this equation gives us Δt = 0.6633 seconds, so it takes approximately 0.6633 seconds for the fish's vertical speed to match its horizontal speed.