Kinematics Forces: Help with Archerfish Targeting & Reaction Time

[Huskies213]

Can anyone Help with this ?

As discussed in Example 4-7, the archerfish hunts by dislodging an unsuspecting insect from its resting place with a stream of water expelled from the fish's mouth. Suppose the archerfish squirts water with a speed of 1.6 m/s at an angle of 59.0° above the horizontal, and aims for a beetle on a leaf 3.0 cm above the water's surface.

-At what horizontal distance from the beetle should the archerfish fire if it is to hit its target in the least time?

-How much time will the beetle have to react?

Thanks

 

[moose]

Break up the speed into x and y components. You have an equation which solves for y height. You can use that one to solve for the time. Then, you should know how to do the rest ;)

 

[quicknote]

for your question. Kinematics and forces play a crucial role in the successful targeting and reaction time of the archerfish. To determine the optimal horizontal distance for the fish to fire at the beetle, we need to consider the projectile motion of the water stream and the height of the beetle above the water's surface. Using the given values of the initial velocity (1.6 m/s) and launch angle (59.0°), we can calculate the horizontal distance using the equation x = (v0^2 sin2θ)/g, where v0 is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity (9.8 m/s^2). This gives us a horizontal distance of approximately 0.74 meters.

As for the reaction time of the beetle, we can use the equation t = 2v0 sinθ/g to calculate the time it takes for the water stream to reach the beetle. Plugging in the values, we get a reaction time of approximately 0.17 seconds. This means the beetle has only 0.17 seconds to react and potentially avoid being hit by the water stream.

It is important to note that these calculations are based on ideal conditions and do not take into account factors such as air resistance and the archerfish's accuracy. However, they provide a good estimate of the targeting and reaction time for the archerfish in this scenario. I hope this helps with your understanding of kinematics and forces in the context of the archerfish's hunting behavior.