A child in danger of drowning in a river is being carried downstream by a current that has a speed of 2.60km/h. The child is 0.615km from shore and 0.815km upstream of a boat landing when a rescue boat sets out. If the boat proceeds at its maximum speed of 21.2km/h relative to the water, what heading relative to the shore should the captain take?

What angle (in degrees) does the boat velocity make with the shore?

How long does it take the boat to reach the child?

I tried drawing it out,but I think I am doing it wrong.

To solve this problem, we need to break it down into smaller components and analyze the velocities involved. I'll guide you step by step.

1. Draw a diagram to visualize the situation:
- Draw a river with a current flowing to the right (downstream).
- Mark a point to represent both the child and the boat landing.
- Label the distance from the child to the boat landing as "0.815 km."
- Draw a line perpendicular to the riverbank to represent the shore.
- Label the distance between the child and the shore as "0.615 km."
- Leave some space to represent the boat's path.

2. Analyze the velocities:
- The current's speed is given as 2.60 km/h downstream.
- The boat's maximum speed relative to the water is 21.2 km/h.

3. Find the boat's true speed relative to the shore:
- The boat's true speed can be determined by adding or subtracting the current's speed, depending on the direction.
- Since the boat is going upstream, subtract the current's speed from the boat's speed: (21.2 km/h - 2.60 km/h) = 18.6 km/h.

4. Determine the heading relative to the shore:
- The heading is the angle between the boat's velocity vector and the line perpendicular to the shore.
- To find this angle, use the tangent function: tan(angle) = (current's speed)/(boat's true speed).
- Plug in the values: tan(angle) = (2.60 km/h) / (18.6 km/h).
- Solve for the angle using inverse tangent (tan^-1) on a calculator.

5. Calculate the time it takes for the boat to reach the child:
- The distance between the child and the shore needs to be traveled upstream.
- Use the equation: Time = Distance / Speed.
- Plug in the values: Time = (0.615 km) / (18.6 km/h).

By following these steps, you should be able to find the heading angle and the time it takes for the boat to reach the child.