# Rescuing a Child in Danger: Calculating the Optimal Path

• Naeem
In summary, we need to use Pythagoras Theorem to solve for the distance the boat travels from the dock to reach the child in the Merimac river. Taking into account the speed of the boat and the current, we can use the Pythagorean Theorem to find the distance x, which is approximately 2.33 km.
Naeem
Q. A child is in danger of drowning in the Merimac river. The Merimac river has a current of 3.1 km/hr to the east. The child is 0.6 km from the shore and 2.5 km upstream from the dock. A rescue boat with speed 24.8 km/hr (with respect to the water) sets off from the dock at the optimum angle to reach the child as fast as possible. How far from the dock does the boat reach the child?

I know in this problem we need to use Pythagoras Theorem, to solve for the right triangle that is obtained. Not able to find one of the variables.

Don't know where I am going wrong,

Any insights, or better ideas are appreciated to this problem.

Let x be the distance the boat travels from the dock. Since the speed of the boat is given with respect to the water, we need to take into account the speed of the current. The total speed of the boat is given by:Speed of boat + Speed of current = 24.8 + 3.1 = 27.9 km/hrNow, using the Pythagorean Theorem, we can find the distance the boat travels from the dock:x^2 + (2.5)^2 = (0.6 + x)^2Solving for x, we get:x = 2.33 km

First, let's start by drawing a diagram to visualize the situation. We have a child in the river, 0.6 km from the shore and 2.5 km upstream from the dock. The river has a current of 3.1 km/hr to the east and the rescue boat has a speed of 24.8 km/hr.

Now, let's label the variables we know and the ones we need to find. We know the distance from the shore to the child (0.6 km), the distance from the dock to the child (2.5 km), and the speed of the rescue boat (24.8 km/hr). We need to find the distance from the dock to where the boat reaches the child, which we will label as x in our diagram.

Next, let's use the Pythagorean theorem to set up an equation. In this case, we have a right triangle with sides of 0.6 km and x km, and a hypotenuse of 2.5 km. This gives us the equation:

(0.6)^2 + x^2 = (2.5)^2

Simplifying this, we get:

0.36 + x^2 = 6.25

Subtracting 0.36 from both sides, we get:

x^2 = 5.89

Taking the square root of both sides, we get:

x = 2.43 km

Therefore, the boat reaches the child at a distance of 2.43 km from the dock.

I hope this helps clarify any confusion. Remember, drawing a diagram and labeling variables can often make a problem easier to visualize and solve. Good luck!

## What is the optimal path for rescuing a child in danger?

The optimal path for rescuing a child in danger depends on various factors such as the location of the child, the type of danger they are in, and the available resources. It is important to carefully assess the situation and gather as much information as possible before determining the optimal path.

## How do you calculate the optimal path for rescuing a child in danger?

Calculating the optimal path for rescuing a child in danger involves using mathematical algorithms and models to analyze the available data and determine the most efficient and effective route. This can include considering factors such as distance, terrain, and potential obstacles.

## What are some common challenges in rescuing a child in danger?

There are many challenges that may arise when rescuing a child in danger, including time constraints, limited resources, and unpredictable conditions. It is important to have a well-developed plan and be prepared to adapt to unexpected circumstances.

## How can technology be used to aid in rescuing a child in danger?

Technology can play a crucial role in rescuing a child in danger. For example, GPS tracking devices and drones can be used to locate the child and determine the most efficient path for rescue. Communication devices can also be used to coordinate efforts and gather information in real-time.

## What steps should be taken after rescuing a child in danger?

After rescuing a child in danger, it is important to assess their physical and emotional well-being and provide any necessary medical attention. It is also important to debrief and gather information about the rescue operation to improve future rescue efforts. Additionally, the child's safety and well-being should be monitored in the days following the rescue.

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