Question

СРОЧНО!!!!! При переправе через реку шириной 60 м надо попасть в точку, лежащую на 80 м ниже течения. За какое минимально возможное время рулевой доплывет до цели, если скорость моторной лодки 8 м/с, а скорость течения 2 м/с ?

Answer 1

Вот лови не благодари

Answer 2

To find the minimum time required for the helmsman to reach the point on the opposite side of the river, we need to consider the effect of the river's current on the boat's motion. The boat's speed relative to the ground will be affected by the speed and direction of the river's current.

Let's break down the problem and calculate the time required step by step:

Given Information:

- Width of the river: 60 m - Target point is 80 m downstream from the starting point - Boat's speed: 8 m/s - River's current speed: 2 m/s

Approach:

To minimize the time taken, the helmsman should steer the boat at an angle that compensates for the river's current. By doing so, the boat will follow a path that is perpendicular to the current, resulting in the shortest time to reach the target point.

Calculation:

1. Calculate the effective speed of the boat relative to the ground: - The effective speed is the vector sum of the boat's speed and the river's current speed. - The boat's speed relative to the ground is given by the formula: sqrt(boat_speed^2 - current_speed^2). - Substituting the given values, we get: sqrt(8^2 - 2^2) = sqrt(60) = 7.746 m/s.

2. Calculate the time required to cross the river: - The time required to cross the river is given by the formula: crossing_time = distance / effective_speed. - Substituting the given values, we get: crossing_time = 60 m / 7.746 m/s = 7.746 seconds.

3. Calculate the time required to travel downstream: - The time required to travel downstream is given by the formula: downstream_time = distance / boat_speed. - Substituting the given values, we get: downstream_time = 80 m / 8 m/s = 10 seconds.

4. Calculate the total time required to reach the target point: - The total time required is the sum of the crossing time and the downstream time. - Substituting the calculated values, we get: total_time = crossing_time + downstream_time = 7.746 seconds + 10 seconds = 17.746 seconds.

Therefore, the helmsman will take a minimum of approximately 17.746 seconds to reach the target point.

Please note that this calculation assumes a straight-line path and does not account for factors such as wind or other forces that may affect the boat's motion.