Kinematics question using vectors

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Discussion Overview

The discussion revolves around a kinematics problem involving vectors, specifically the scenario of a rescue boat attempting to reach a child in a river with a current. Participants are exploring how to determine the optimum angle for the boat's path to minimize the time taken to reach the child, as well as the time required for the journey.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant presents the problem setup, including distances and speeds, and expresses uncertainty about how to find the angle.
  • Another participant questions whether the angle referred to is the optimum angle or simply any angle in the diagram, suggesting the need for clearer labeling of points in the scenario.
  • A different participant notes that the original question does not specify "optimum," raising doubt about the assumption that the angle should be optimized.
  • One participant proposes that if the boat cannot change its angle during the trip, there would be a unique angle that allows the boat to reach the child, leading to a system of equations involving the angle and time.
  • There is a suggestion to define the angle as ##\theta## and to derive the velocities of the boat in both the x and y directions to create equations for the distances traveled.

Areas of Agreement / Disagreement

Participants express uncertainty about the interpretation of the problem, particularly regarding the term "optimum" and the implications for the angle of the boat's path. There is no consensus on the approach to solving the problem or the assumptions that should be made.

Contextual Notes

Participants highlight potential ambiguities in the problem statement, such as the lack of clarity on whether the angle must be optimized or if it is simply a matter of finding any angle. There is also mention of the possibility of a system of equations having one or no solutions, depending on the constraints of the problem.

Ofir12
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A child is in danger of drowning in the river. The river has a current of 2.5 km/hr . The child is 0.6 km from the shore. A rescue boat with speed 20.0 km/hr (with respect to the water) ,located 0.8km downstream, sets off from the shore.
What would be the optimum angle (shore -> boat ) to reach the child as fast as possible ?
And how long will it take to the boat to reach him?

I'm not sure if this is the correct way to draw this :
river-rescue-gif.gif


The Attempt at a Solution



a = 0.6 km
b = 0.8 km

v = 20.0km
u = 2.5km

c = √(a² + b²)

how do I find the angle?

I feel a little bit lost, your help is appriciated.
Thanks.
 

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Ofir12 said:
how do I find the angle?
The optimum angle or some angle in the diagram? For reference, it would be handy to label some points, like B for launch point of boat, etc.
What are your thoughts on the optimisation?
 
I'm not sure if this is the right way to draw this, and how to approach the question.
I know that I'm looking for an angle between 2 vectors (shore and boat).
Actually they didn't mention the word "optimum" in the question, they just asked what is the angle. (I assumed that it should be optimum, buy maybe I am wrong)
 
Well this problem is kind of strange for me as to what the problem wants. If the boat isn't allowed to change angle during its trip, then there is only one possible angle (there will be a system of two equations with two unknowns, the angle and the time , this system might have one solution or none) for which the boat reaches the child.

I suggest for starting, that you assume that ##\theta## is the angle. Find the velocities ##v_x## and ##v_y## of the boat, and make two equations for the distance traveled ##s_x## and ##s_y## in each axis.
 

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