A pelican flying along a horizontal path drops
a fish from a height of 3.1 m. The fish travels
6.4 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 3.1meters?
then, use that time to calculate horizontal velocity distance/time
To find the pelican's initial speed, we can use the principle of conservation of energy.
When the fish is dropped, it has potential energy due to its height, given by the equation U = mgh, where U is potential energy, m is the mass, g is the acceleration due to gravity, and h is the height.
The potential energy is converted into kinetic energy as the fish falls. The kinetic energy is given by the equation K = (1/2)mv^2, where K is kinetic energy, m is the mass, and v is the velocity.
Since we have both the height and horizontal distance, we can calculate the time the fish takes to fall using the equation d = (1/2)gt^2, where d is the distance, g is the acceleration due to gravity, and t is the time.
In this case, the fish has fallen 3.1 m vertically, so h = 3.1 m. The horizontal distance travelled, d, is 6.4 m. The acceleration due to gravity, g, is 9.81 m/s^2.
Using the equation d = (1/2)gt^2, we can solve for t:
6.4 m = (1/2)(9.81 m/s^2)t^2
Rearranging the equation, we get:
12.8 m = (9.81 m/s^2)t^2
Dividing both sides by 9.81 m/s^2, we get:
t^2 = 1.306
Taking the square root of both sides, we get:
t = 1.142 s
Now that we know the time it takes for the fish to fall, we can calculate its velocity using the equation v = gt:
v = 9.81 m/s^2 * 1.142 s
v ≈ 11.2 m/s
Therefore, the initial speed of the pelican is approximately 11.2 m/s.