# Solve River Rescue Problem: How Far from Dock Does Boat Reach Child?

• rgalvan2
In summary, the child is in danger of drowning in the Merimac river, 0.6 km from the shore and 2.5 km upstream from the dock. A rescue boat with speed 24.8 km/hr sets off from the dock at an optimum angle to reach the child. The hardest calculation is determining the time it takes for the swimmer to be rescued and thus the time the dock is moving. To solve for the distance from the dock, the Pythagorean Theorem is used, giving a distance of 2.57 km. Plugging this into the equation d=vt, the time it takes for the swimmer to be rescued is found to be 0.1 hr. However, the computer
rgalvan2
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?

https://online-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys211/fall08/homework/02/IE_rescue/boat.gif

https://online-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys211/fall08/homework/02/IE_rescue/help/help/help/help_t/pic6.gif

The hardest calculation in this problem is to determine the time it takes for the swimmer to be rescued (and thus the time the dock is moving).
What is t?

So I need to use Pythagorean Theorem to find z. I found it to be 2.57. Then I used d=vt to find the time it takes for the swimmer to be rescued which is the time the dock is moving. So for v, the problem says to use the boat's velocity which is 24.8. I get t=.104 hr. It keeps saying I'm wrong. What am i doing wrong? Help Please!

Last edited by a moderator:
Why are you treating the dock as moving? The child is not motionless. The child is also floating down river at 3.1 km/hr. I think this problem is very simple if you set your frame of reference in the river. If you are entering the solution into a computer, are you expected to give the time in hours or minutes?

The help links are making me use the water/child as the reference frame. The time is entered in hours.

Can you clarify the question again? Are you looking for distance from the dock or time?
In my understanding of the question, when the boat is released from the dock, the boat is stationary with respect to the child. Then it's a matter of just directly driving to the child.

rgalvan2 said:
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?

https://online-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys211/fall08/homework/02/IE_rescue/help/help/help/help_t/pic6.gif

The hardest calculation in this problem is to determine the time it takes for the swimmer to be rescued (and thus the time the dock is moving).
What is t?

So I need to use Pythagorean Theorem to find z. I found it to be 2.57. Then I used d=vt to find the time it takes for the swimmer to be rescued which is the time the dock is moving. So for v, the problem says to use the boat's velocity which is 24.8. I get t=.104 hr. It keeps saying I'm wrong. What am i doing wrong? Help Please!

What distance (d from your figure) did you calculate? Is that what's asked?

Last edited by a moderator:
I am trying to solve for d. This is just a help link, it just walks me through what I need to do. This help section is having me solve for z and using that in the equation d=vt as the distance. Since we are using the boat's speed, we have v and the distance z. I solved for t giving me .1 hours. This specific help tells me to find z by Pythagorean Theorem which I did: $$\sqrt{2.52 + .62}$$ = 2.57=z. So I plugged z into d=vt: 2.57km=24.8km/hr(t)
t=2.57km/24.8km/hr=.1hr. The computer is not accepting my answer. Am I making a stupid mistake or what?

rgalvan2 said:
I am trying to solve for d. This is just a help link, it just walks me through what I need to do. This help section is having me solve for z and using that in the equation d=vt as the distance. Since we are using the boat's speed, we have v and the distance z. I solved for t giving me .1 hours. This specific help tells me to find z by Pythagorean Theorem which I did: $$\sqrt{2.52 + .62}$$ = 2.57=z. So I plugged z into d=vt: 2.57km=24.8km/hr(t)
t=2.57km/24.8km/hr=.1hr. The computer is not accepting my answer. Am I making a stupid mistake or what?

I understand. I get that 2.57 is the distance through the water. But isn't the answer they seek the distance from the dock at the time of rescue - at .1 hr? At a time when the x-leg is .1 hr shorter = .31 km shorter?

## What is the River Rescue Problem and why is it important?

The River Rescue Problem is a hypothetical situation in which a boat needs to reach a child who has fallen into a river, and it is important because it demonstrates the use of mathematical and scientific principles to solve real-world problems.

## What are the factors that affect how far the boat can reach the child?

The factors that affect how far the boat can reach the child include the speed of the boat, the direction and strength of the current, the distance between the dock and the child, and the angle at which the boat must travel to reach the child.

## How can mathematical equations be used to solve the River Rescue Problem?

Mathematical equations such as the Pythagorean theorem and the law of sines can be used to calculate the distance between the dock and the child, as well as the distance the boat must travel to reach the child.

## What are some real-world applications of the River Rescue Problem?

The River Rescue Problem has real-world applications in fields such as search and rescue operations, water safety and rescue training, and engineering design for watercraft and river navigation.

## What are some limitations of using mathematical equations to solve the River Rescue Problem?

Some limitations of using mathematical equations to solve the River Rescue Problem include the assumption of ideal conditions and fixed variables, which may not always accurately reflect real-world scenarios. Additionally, human error and environmental factors may also impact the outcome of the rescue operation.

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