Answer:
The height above the waterline that the stream reaches at the horizontal position of the insect is 15 cm.
Explanation:
Please, see the attached figure for a description of the problem.
The motion is parabolic and this is the equation that describes the position of an object in such a motion:
r = (x0 + v0 · t · cos α, y0 + v0 · t · sin α + 1/2 · g · t²)
Where:
r = position vector
x0 = initial horizontal position
v0 = initial velocity
t = time
α = angle of the stream with the waterline
y0 = initial vertical position
g = acceleration due to gravity
First, let´s calculate how much time it takes the stream to reach the horizontal position of 0.27 m. For this, we will use the equation of the x-component of the vector position:
x = x0 + v0 · t · cos α
Since the origin of the reference system is located at the mouth of the fish, x0 = 0. Then:
0.27 m = 3.7 m/s · t · cos 35º
t = 0.27 m /(3.7 m/s · cos 35º)
t = 0.089 s
Now, with this time, we can calulate the vertical position (height) of the stream using the equation for the y-component of the vector "r":
y = y0 + v0 · t · sin α + 1/2 · g · t²
y = 0 m + 3.7 m/s · 0.089 s · sin 35º + 1/2 · (-9.8 m/s²) · (0.089s)²
y = 0.15 m
when the stream reaches 27 cm horizontally, it will reach 15 cm vertically and hit the insect!
