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
d = Vo*t + 0.5g*t^2 = 4.7 m.
0 + 4.9t^2 = 4.7
t^2 = 0.9592
Tf = 0.98 s. = Fall time.
Dx = Xo * Tf = 7.7 m.
Xo * 0.98 = 7.7
Xo = 7.86 m/s. = Initial hor. speed.
To solve this problem, we can use the equations of motion. The horizontal motion of the fish is independent of the vertical motion, so we can focus on the vertical motion only.
We know that the fish is dropped from a height of 4.7 m and it takes some time to reach the water 7.7 m horizontally away.
First, let's find the time it takes for the fish to fall from 4.7 m. We can use the equation:
d = (1/2) * g * t^2
Where:
d = vertical distance (4.7 m)
g = acceleration due to gravity (9.81 m/s^2)
t = time taken
Plugging in the values, we have:
4.7 = (1/2) * 9.81 * t^2
Simplifying the equation gives us:
9.81t^2 = 9.4
Dividing both sides by 9.81:
t^2 ≈ 0.9591
Taking the square root of both sides:
t ≈ √0.9591
t ≈ 0.9798 s
Now we can find the pelican's initial vertical velocity. We can use the equation:
v = g * t
Where:
v = initial vertical velocity
g = acceleration due to gravity (9.81 m/s^2)
t = time taken (0.9798 s)
Plugging in the values, we have:
v = 9.81 * 0.9798
v ≈ 9.6124 m/s
Finally, we can find the pelican's initial speed using the horizontal distance traveled by the fish. We can use the equation:
v = d / t
Where:
v = initial speed
d = horizontal distance (7.7 m)
t = time taken (0.9798 s)
Plugging in the values, we have:
v = 7.7 / 0.9798
v ≈ 7.8680 m/s
Therefore, the pelican's initial speed is approximately 7.8680 m/s.
To find the pelican's initial speed, we can use the principles of projectile motion. Let's break down the problem step by step:
1. Firstly, we need to understand that the vertical motion (downward motion of the fish) is governed by the acceleration due to gravity, which is 9.81 m/s^2.
2. We can use the equation of motion for vertical motion:
Δy = v₀t + (1/2)at²
where Δy is the displacement in the vertical direction (negative since the fish is falling downward), v₀ is the initial vertical velocity, t is the time of flight, and a is the acceleration due to gravity.
3. The displacement in the vertical direction, Δy, is given as -4.7 m because it is downward.
4. We can also use the equation of motion for horizontal motion:
Δx = v₀x * t
where Δx is the horizontal displacement, v₀x is the initial horizontal velocity (same as the pelican's initial speed), and t is the time of flight.
5. The horizontal displacement, Δx, is given as 7.7 m.
6. Since the time of flight is the same for both vertical and horizontal motion, we can equate the two equations we derived:
Δx = v₀x * t = v₀x * (2Δy / a) (from the equation Δy = v₀t + (1/2)at²)
7. Rearranging the equation, we get:
v₀x = (Δx * a / (2 * Δy))^0.5
8. Plugging in the given values:
Δx = 7.7 m
Δy = -4.7 m
a = 9.81 m/s^2
9. Calculating the initial speed of the pelican:
v₀x = (7.7 * 9.81 / (2 * -4.7))^0.5
After you evaluate the expression, you will find that the pelican's initial speed is approximately 9.05 m/s.