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(a) What are the position and velocity of the water droplet as a function of time and the position and velocity of the bug as a function of time, valid for times between when the fish shoots and when the water hits the bug? Use a coordinate system in which the origin is located at the fish's mouth, the positive a direction is to the right, and the positive y direction is upwards. Your answer may contain any or all of h. vo. d. g. t. i ("hati"), 3("hatj"), and 0. Fwater (t) = Uwater (t) = Flug (t) = Vrug (t)= (b) At what horizontal distance, d, from the branch, and at what angle above horizontal, 0, should the archerfish shoot? Express your answer in terms of vo. g. and has needed. d = 0-

(a) What are the position and velocity of the water droplet as a function of time and the position and velocity of the bug as a function of time, valid for times between when the fish shoots and when the water hits the bug? Use a coordinate system in which the origin is located at the fish's mouth, the positive a direction is to the right, and the positive y direction is upwards. Your answer may contain any or all of h. vo. d. g. t. i ("hati"), 3("hatj"), and 0. Fwater (t) = Uwater (t) = Flug (t) = Vrug (t)= (b) At what horizontal distance, d, from the branch, and at what angle above horizontal, 0, should the archerfish shoot? Express your answer in terms of vo. g. and has needed. d = 0-

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The banded archerfish is a species of fish that lives in mangrove estuaries in Asia and Oceania. It has a unique and highly effective hunting strategy: it shoots an incredibly precise stream of water out of its mouth at almost ten meters per second, knocking insects and other small animals into the water from nearby branches! Pom Fbug (t) Ө = Our hero, a hungry archerfish, has spotted a big, delicious bug sitting on a branch a height ħ above the surface of the water. The archerfish can shoot its water jet at a speed of vo. The archerfish wants to knock the bug sideways off of the branch, so it decides to shoot so that its water jet is moving horizontally at the moment when it strikes the bug. The final goal of this problem is to find the horizontal distance, d, from the branch, and the angle above horizontal, 0, at which archerfish should shoot. d (a) What are the position and velocity of the water droplet as a function of time and the position and velocity of the bug as a function of time, valid for times between when the fish shoots and when the water hits the bug? Use a coordinate system in which the origin is located at the fish's mouth, the positive a direction is to the right, and the positive y direction is upwards. Your answer may contain any or all of h, vo, d. g, t, î ("hati"), 3 ("hatj"), and 0. water (t) = Vwater (t) = h Vrug (t) = Calculator ▸
Transcribed Image Text:The banded archerfish is a species of fish that lives in mangrove estuaries in Asia and Oceania. It has a unique and highly effective hunting strategy: it shoots an incredibly precise stream of water out of its mouth at almost ten meters per second, knocking insects and other small animals into the water from nearby branches! Pom Fbug (t) Ө = Our hero, a hungry archerfish, has spotted a big, delicious bug sitting on a branch a height ħ above the surface of the water. The archerfish can shoot its water jet at a speed of vo. The archerfish wants to knock the bug sideways off of the branch, so it decides to shoot so that its water jet is moving horizontally at the moment when it strikes the bug. The final goal of this problem is to find the horizontal distance, d, from the branch, and the angle above horizontal, 0, at which archerfish should shoot. d (a) What are the position and velocity of the water droplet as a function of time and the position and velocity of the bug as a function of time, valid for times between when the fish shoots and when the water hits the bug? Use a coordinate system in which the origin is located at the fish's mouth, the positive a direction is to the right, and the positive y direction is upwards. Your answer may contain any or all of h, vo, d. g, t, î ("hati"), 3 ("hatj"), and 0. water (t) = Vwater (t) = h Vrug (t) = Calculator ▸
Our hero, a hungry archerfish, has spotted a big, delicious bug sitting on a branch a height ħ above the surface of the water. The archerfish can shoot its water jet at a speed of vo. The archerfish wants to knock the bug sideways off of the branch, so it decides to shoot so that its water jet is moving horizontally at the moment when it strikes the bug. The final goal of this problem is to find the horizontal distance, d, from the branch, and the angle above horizontal, 0, at which archerfish should shoot. (a) What are the position and velocity of the water droplet as a function of time and the position and velocity of the bug as a function of time, valid for times between when the fish shoots and when the water hits the bug? Use a coordinate system in which the origin is located at the fish's mouth, the positive a direction is to the right, and the positive y direction is upwards. Your answer may contain any or all of h, vo, d. g, t, î ("hati"), 3 ("hatj"), and 0. Fwater (t) = Vwater (t) * bug (t) d d = Vbug (t)= (b) At what horizontal distance, d, from the branch, and at what angle above horizontal, 0, should the archerfish shoot? Express your answer in terms of vo, g, and has needed. 0 = Calculator ▸
Transcribed Image Text:Our hero, a hungry archerfish, has spotted a big, delicious bug sitting on a branch a height ħ above the surface of the water. The archerfish can shoot its water jet at a speed of vo. The archerfish wants to knock the bug sideways off of the branch, so it decides to shoot so that its water jet is moving horizontally at the moment when it strikes the bug. The final goal of this problem is to find the horizontal distance, d, from the branch, and the angle above horizontal, 0, at which archerfish should shoot. (a) What are the position and velocity of the water droplet as a function of time and the position and velocity of the bug as a function of time, valid for times between when the fish shoots and when the water hits the bug? Use a coordinate system in which the origin is located at the fish's mouth, the positive a direction is to the right, and the positive y direction is upwards. Your answer may contain any or all of h, vo, d. g, t, î ("hati"), 3 ("hatj"), and 0. Fwater (t) = Vwater (t) * bug (t) d d = Vbug (t)= (b) At what horizontal distance, d, from the branch, and at what angle above horizontal, 0, should the archerfish shoot? Express your answer in terms of vo, g, and has needed. 0 = Calculator ▸
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