Answer:Solve Archer Fish Physic Problem: Find θ0

[sagaradeath]

Physic Problem. Please Help!

Homework Statement

Upon spotting an insect on a twig overhanging water, an archer fish squirts water drops at the insect to knock it into the water. Although the fish sees the insect along a straight-line path at angle φ and distance d, a drop must be launched at a different angle θ0 if its parabolic path is to intersect the insect. If φ = 35.0° and d = 0.900 m what θ0 is required for the drop to be at the top of the parabolic path when it reaches the insect?

Figure:
.........… insect on twig
.........…
.........…
.........…
.........… /
.........…
.........…
.........… φ
________________/_______________
......x=o> archer fish
2 years ago

Figure:
.....* insect on twig
....../
...../
....../
.....d /
.../
..../
.../ φ
____/___________
x=o> archer fish

Homework Equations

The Attempt at a Solution

Since the water droplets are at the top of their trajectory you can write:

h = (1/2)gt^2

h = height of insect = 0.9sin(35) = 0.516 m
g = acceleration of gravity = 9.8 m/s^2
t = time to fall from the branch to the water

t^2 = 2h/g
t = SQRT(2h/g)
t = SQRT(2*0.516/9.8) = 0.32450 seconds

Although this is the time to fall from the branch to the water it is also the time it takes to go from the water to the branch and this we can use below.

In order to find the angle phi (P) we can use the fact that tan(P) = v/u where:
v = initial vertical velocity of the water
u = initial horizontal velocity of the water

As far as u it is the horizontal distance divided by the time just calculated so:
horizontal distance = 0.9cos(35) = 0.73723 m
u = 0.73723/0.3245 = 2.27 m/s

We now need v. For this use:
v = gt = (9.8)(0.3245) = 3.1801 m/s

tan(P) = v/u = 3.1801/2.27 = ?

 

[sagaradeath]

is this right?
this equation should get me the answer but i think I am doing it wrong

tan(P) = v/u = 3.1801/2.27 = 1.4009

 

[sagaradeath]

can anyone help me with the answer to this problem?

 

[gneill]

If in fact the problem author did indeed intend the distance d supplied to mean the radial distance from the fish to the insect (as opposed to the horizontal distance), then you're 99% of the way to the solution; Find the angle corresponding to a tan of 1.4.

 

[rwisz]

?
P = tan^-1(??) = 54.5 deg

The angle theta (T) we seek is the angle the water is shot at. This is the same as the angle the fish sees plus the angle the water is shot at. Thus:
T = 54.5 + 35 = 89.5 deg

Therefore, the angle θ0 required for the drop to be at the top of the parabolic path when it reaches the insect is 89.5 degrees.