A small fish is dropped by a pelican that is
rising steadily at 0.63 m/s.
After 2.5 s, what is the velocity of the fish?
The acceleration of gravity is 9.81 m/s2.
Answer in units of m/s
To determine the velocity of the fish, we need to calculate the change in its velocity due to gravity over the given time.
The pelican is rising steadily, so it has a constant upward velocity of 0.63 m/s. However, the fish is subject to the acceleration of gravity, which has a magnitude of 9.81 m/s² and acts in the downward direction.
Given that the fish is in free fall, we can assume that the only force acting on it is gravity. Therefore, its acceleration due to gravity is the same as the acceleration of gravity, which is 9.81 m/s².
Using the kinematic equation:
vf = vi + at
where
vf is the final velocity,
vi is the initial velocity,
a is the acceleration, and
t is the time elapsed,
we can substitute the given values to find the final velocity of the fish after 2.5 s.
vi = 0 m/s (since the fish is dropped by the pelican and initially has zero speed)
a = 9.81 m/s² (acceleration due to gravity)
t = 2.5 s (time elapsed)
Using the formula:
vf = 0 + (9.81)(2.5)
vf = 24.525 m/s
Therefore, after 2.5 seconds, the velocity of the fish is approximately 24.525 m/s.
To find the velocity of the fish after 2.5 seconds, we can use the acceleration due to gravity and the time elapsed.
First, we need to determine the displacement of the fish during this time. The displacement is given by the formula:
s = ut + (1/2)gt^2
where:
s = displacement
u = initial velocity
g = acceleration due to gravity
t = time
In this case, the initial velocity of the fish is 0 m/s because it was dropped. So we can simplify the formula to:
s = (1/2)gt^2
Next, we can calculate the displacement of the fish during the 2.5 seconds:
s = (1/2)(9.81 m/s^2)(2.5 s)^2
= (1/2)(9.81 m/s^2)(6.25 s^2)
= 30.65625 m
Now that we have the displacement, we can calculate the final velocity using the formula:
v = u + gt
Since the initial velocity (u) is 0 m/s, the formula simplifies to:
v = gt
Now we can substitute the values into the formula and find the velocity:
v = (9.81 m/s^2)(2.5 s)
= 24.525 m/s
Therefore, the velocity of the fish after 2.5 seconds is 24.525 m/s.