A pelican flying along a horizontal path drops
a fish from a height of 3.1 m. The fish travels
8.4 m horizontally before it hits the water
below.
What was the pelican’s initial speed? The
acceleration of gravity is 9.81 m/s
2
.
Answer in units of m/s
how long does it take to fall 3.1m on Earth?
3.1=1/2 g t^2 solve for time t.
speed=8.4/t m/s
To find the pelican's initial speed, we can use the principle of conservation of energy. The potential energy of the fish at the beginning is converted to the kinetic energy of the fish just before it hits the water.
Let's break down the problem into two parts - vertical and horizontal.
1. Vertical motion:
The potential energy (PE) of the fish is given by its height above the water, which is equal to the mass of the fish (m) multiplied by the acceleration due to gravity (g) multiplied by the height (h).
PE = m * g * h
2. Horizontal motion:
The horizontal distance traveled (d) by the fish is equal to the product of its horizontal velocity (v) and the time taken (t).
d = v * t
Since the only force acting on the fish horizontally is its initial velocity, there is no acceleration in the horizontal direction.
Therefore, we can use the equations of motion for constant velocity:
d = v * t
where t is the time of flight of the fish.
We can calculate the time taken by the fish to hit the water using the vertical motion. The total distance traveled along the vertical direction is equal to the height of the fish dropped.
h = 3.1 m
Using the equation of motion for free-falling bodies:
h = 0.5 * g * t^2
Rearranging the equation to solve for t gives:
t = sqrt(2h / g)
Substituting the given values:
t = sqrt(2 * 3.1 / 9.81) = 0.8 s (approximately)
Now, we can substitute the value of t into the equation for horizontal motion:
8.4 m = v * 0.8 s
Solving for v:
v = 8.4 m / 0.8 s = 10.5 m/s
Therefore, the pelican's initial speed was approximately 10.5 m/s.