Question

Акула, раскрыв пасть площадью 540 см², плывет со скоростью 9.2 м/с. Навстречу ей плывет косяк рыб со скоростью 1.9 м/с. Концентрация рыб в косяке составляет в среднем 20 рыб на кубометр. Найдите: 1) Какое в среднем число рыб будет попадать в пасть акуле в секунду, если скорость акулы и косяка будет оставаться неизменной? 2) Во сколько раз вырастет это число, если скорость акулы возрастет вдвое? Ответы приведите с точностью до сотых

Answer 1

Переводим квадратные сантиметры в квадратные  метр 1 квадрометре - 10000 квадро см то есть у акулы пасть 0,05 квадратных метра и кушает она рыб со скоростью 16 рыб 0,05 кв метра=0,8  рыб съест акула, когда пройдет 1 метр данная акула приближается к косяку рыб со скоростью 9+1,8=10,8 м/с,а значит съедает рыб со скоростью 10,8х0,8=8,64 рыбы в секунду Если скорость акулы возрастет в двое, то количество съедаемых рыб в минуту будет (2х9 +1,8)х0,8= 15,84 рыбы в секунду

Answer 2

Calculation of the Number of Fish Caught by the Shark

To calculate the number of fish that will be caught by the shark in one second, we need to consider the area covered by the shark's mouth and the concentration of fish in the school.

Given: - The area of the shark's mouth is 540 cm². - The shark swims at a speed of 9.2 m/s. - The school of fish swims towards the shark at a speed of 1.9 m/s. - The concentration of fish in the school is 20 fish per cubic meter.

To find the number of fish caught by the shark in one second, we need to calculate the volume of water passing through the shark's mouth in one second and then multiply it by the concentration of fish in the school.

Calculation 1: Number of Fish Caught with Unchanged Shark Speed

To calculate the volume of water passing through the shark's mouth in one second, we need to multiply the area of the shark's mouth by the relative speed of the shark and the school of fish.

Relative speed = shark's speed - school of fish's speed

Relative speed = 9.2 m/s - 1.9 m/s = 7.3 m/s

Volume of water passing through the shark's mouth in one second = area of the shark's mouth * relative speed

Volume of water passing through the shark's mouth in one second = 540 cm² * 7.3 m/s = 540 * 0.0001 m² * 7.3 m/s = 0.03942 m³/s

Now, we can calculate the number of fish caught by the shark in one second by multiplying the volume of water passing through the shark's mouth by the concentration of fish in the school.

Number of fish caught by the shark in one second = volume of water passing through the shark's mouth in one second * concentration of fish in the school

Number of fish caught by the shark in one second = 0.03942 m³/s * 20 fish/m³ = 0.7884 fish/s

Therefore, the average number of fish that will be caught by the shark in one second, with the shark's speed and the school of fish's speed remaining unchanged, is approximately 0.79 fish/s.

Calculation 2: Number of Fish Caught with Doubled Shark Speed

To calculate the number of fish caught by the shark if its speed is doubled, we need to recalculate the volume of water passing through the shark's mouth in one second using the new shark speed.

New shark speed = 2 * 9.2 m/s = 18.4 m/s

Volume of water passing through the shark's mouth in one second = area of the shark's mouth * relative speed

Volume of water passing through the shark's mouth in one second = 540 cm² * (18.4 m/s - 1.9 m/s) = 540 * 0.0001 m² * 16.5 m/s = 0.0891 m³/s

Now, we can calculate the number of fish caught by the shark in one second by multiplying the volume of water passing through the shark's mouth by the concentration of fish in the school.

Number of fish caught by the shark in one second = volume of water passing through the shark's mouth in one second * concentration of fish in the school

Number of fish caught by the shark in one second = 0.0891 m³/s * 20 fish/m³ = 1.782 fish/s

Therefore, if the shark's speed is doubled, the average number of fish that will be caught by the shark in one second will be approximately 1.78 fish/s.

In summary: 1) The average number of fish that will be caught by the shark in one second, with the shark's speed and the school of fish's speed remaining unchanged, is approximately 0.79 fish/s. 2) If the shark's speed is doubled, the average number of fish that will be caught by the shark in one second will be approximately 1.78 fish/s.