Question

A hawk in level flight 135m above the ground drops the fish it caught. If the hawk horizontal speed is 20m/s, how far ahead of the drop point will the fish land

Answer 1

Find how long it will take the fish to hit the ground

Answer 2

The fish will land approximately 105 meters ahead of the drop point.

How to determine how far ahead of the drop point the fish will land?

To determine the horizontal distance the fish travels before hitting the ground after being dropped by the hawk, we'll use the equations of motion.

Given:

Vertical distance fallen by the fish (\(h\)) = 135 meters

Hawk's horizontal speed (\(v\)) = 20 m/s

Acceleration due to gravity (\(g\)) ≈ 9.81 m/s²

First, let's find the time it takes for the fish to fall
`(\(t\))`:

`\[ t = \sqrt{(2h)/(g)} \]`

`\[ t = \sqrt{(2 * 135)/(9.81)} \]`

`\[ t \approx √(27.486) \approx 5.25 \, \text{s} \]`

Now, using the horizontal speed and time, we can determine the horizontal distance traveled
`(\(d\))` by the fish:

`\[ d = v * t \]`

`\[ d = 20 \, \text{m/s} * 5.25 \, \text{s} \]`

`\[ d \approx 105 \, \text{m} \]`

Hence, the fish will land approximately 105 meters ahead of the drop point.