A pelican flying along a horizontal path drops
a fish from a height of 5.0 m. The fish travels
8.5 m horizontally before it hits the water
below.
The acceleration of gravity is 9.81 m/s2 .
a) What was the pelican’s initial speed?
Answer in units of m/s.
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To find the initial speed of the pelican, we can use the kinematic equations of motion.
First, let's list the known values:
Height (h) = 5.0 m
Horizontal distance (d) = 8.5 m
Acceleration due to gravity (g) = 9.81 m/s^2
We need to find the initial speed (u).
The equation that relates distance, initial velocity, time, and acceleration is:
d = ut + (1/2)at^2
Since the pelican drops the fish vertically, the time taken to reach the ground is the same as the time it takes to travel horizontally. We can set the time (t) for both motions equal to each other.
For the vertical motion:
h = (1/2)gt^2
For the horizontal motion:
d = ut
Now we can solve these two equations simultaneously to find the initial velocity (u).
From the vertical motion equation:
5.0 = (1/2)(9.81)t^2
Simplifying:
t^2 = (2 * 5.0) / 9.81
t^2 = 1.019
Taking the square root of both sides:
t = 1.009 s (approx.)
Using the horizontal motion equation:
8.5 = u * (1.009)
Simplifying:
u ≈ 8.4 m/s
Therefore, the pelican's initial speed is approximately 8.4 m/s.
how long to fall?
5 = 4.9 t^2
solve for t
how far horizontal? (same horizontal speed as bird, not horizontal force, fish lands exactly under bird, turn to avoid splash.
8.5 = u t and we know t so get u