A pelican flying along a horizontal path drops

a fish from a height of 4.7 m. The fish travels
7.7 m horizontally before it hits the water
below.
What was the pelican’s initial speed? The
acceleration of gravity is 9.81 m/s2 .
Answer in units of m/s

How long does it take an object to drop 4.7 meters?

How fast does an object have to move to fly 7.7 meters in that amount of time?

To find the pelican's initial speed, we can use the equations of motion. The key information we need is the height from which the fish was dropped and the horizontal distance it traveled before hitting the water.

Let's start by using the equation to calculate the time it takes for the fish to fall from a height of 4.7 m:

Δy = v₀t + (1/2)gt²

Where:
- Δy is the change in vertical distance (4.7 m)
- v₀ is the initial vertical velocity (unknown)
- t is the time it takes for the fish to reach the water (unknown)
- g is the acceleration due to gravity (-9.81 m/s²)

Plugging in the values, we get:

4.7 m = 0t + (1/2)(-9.81 m/s²)t²

Simplifying further, we have:

4.7 m = (-4.905 m/s²)t²

Now, we can solve this equation to find the time it takes for the fish to fall. Rearranging the equation gives:

t² = (4.7 m) / (-4.905 m/s²)

t² ≈ -0.958

Since time cannot be negative, we take the positive square root:

t ≈ √(-0.958) ≈ 0.979 s

Now that we have the time it took for the fish to fall, we can calculate the horizontal component of the initial velocity of the fish using the equation:

Δx = v₀x * t

Where:
- Δx is the horizontal distance traveled by the fish (7.7 m)
- v₀x is the initial horizontal velocity (unknown)
- t is the time it took for the fish to fall (0.979 s)

Plugging in the values, we have:

7.7 m = v₀x * 0.979 s

Solving for v₀x:

v₀x ≈ (7.7 m) / (0.979 s)

v₀x ≈ 7.88 m/s

Therefore, the pelican's initial speed is approximately 7.88 m/s.