Math Model for Archer Fish Spitting Water at Insect

[atomant]

I came across a question involving an archer fish and an insect that has me puzled. The question gives that an archer fish spots an insect dangling on a branch of a tree. The fish can attack by spitting water at it's prey. But it just so happens that just as this fish spits out the water, the insect is startled and drops from the branch. Now the question is what happens to the water that was spat out?..does it miss the insect?, or does it hit regardless?.
The answer given was that it hits the insect regardless of the drop. I do not however understand why this is so?. I have tried to come up with an equation to explain this but no luck so far. All I have so far is that there is an object (the insect) that is falling at a constant rate of g, another object (the water from the fish) traveling towards it with a speed v and the fact that at time t the two objects collide. Is there any way to show this through an equation?

 

[topsquark]

I came across a question involving an archer fish and an insect that has me puzled. The question gives that an archer fish spots an insect dangling on a branch of a tree. The fish can attack by spitting water at it's prey. But it just so happens that just as this fish spits out the water, the insect is startled and drops from the branch. Now the question is what happens to the water that was spat out?..does it miss the insect?, or does it hit regardless?.
The answer given was that it hits the insect regardless of the drop. I do not however understand why this is so?. I have tried to come up with an equation to explain this but no luck so far. All I have so far is that there is an object (the insect) that is falling at a constant rate of g, another object (the water from the fish) traveling towards it with a speed v and the fact that at time t the two objects collide. Is there any way to show this through an equation?

This is similar to the "shoot the monkey" (or for those that like a more animal friendly problem, "shoot the can") problem. Don't think of the water as a stream, but a projectile. As the insect falls, it is accelerated by gravity. As the water moves, it is accelerated by the same amount from where it would be if it traveled in a straight line. (Sorry, I can't do the picture yet!)

In terms of equations, what you need to do to set this up is to write an equation that says where the insect is at a given time. Do the same for a "projectile" (your steam of water) from the fish. What you want to show is that when the projectile gets to the horizontal (x) displacement that the insect is at, that both the insect and projectile have the same vertical (y) displacement.

It isn't a particularly hard problem, but you do need to keep careful track of all the variables involved.

-Dan

 

[kyle8921]

I would approach this question by first understanding the physics involved in this scenario. The archer fish uses a specialized mechanism to propel water out of its mouth at high speeds. This jet of water is able to travel a certain distance before it breaks into droplets due to air resistance. The insect, on the other hand, is falling at a constant rate due to gravity.

To model this situation mathematically, we can use the equation for projectile motion, which takes into account the initial velocity, angle of projection, and the acceleration due to gravity. In this case, the initial velocity is the speed at which the water leaves the fish's mouth, and the angle of projection is the direction in which the water is aimed.

We also need to consider the distance between the fish and the insect, as well as the height of the branch from which the insect is hanging. This will give us the time it takes for the water to reach the insect and the distance it travels before it hits the insect.

However, we also need to take into account the speed at which the insect is falling. This means that the insect will move a certain distance in the time it takes for the water to reach it, potentially changing its position and making it harder to hit.

In conclusion, while it is possible to model this scenario mathematically, it would require a lot of variables and assumptions to accurately predict the outcome. It is also important to keep in mind that in real-life situations, there are many factors that can affect the accuracy of a mathematical model. Therefore, it is always best to conduct experiments and collect data to understand the behavior of the archer fish and its ability to hit its target with water.