Kinematics question using vectors

AI Thread Summary
The discussion revolves around a kinematics problem involving a child in a river and a rescue boat. The river's current is 2.5 km/hr, and the boat travels at 20.0 km/hr relative to the water, starting 0.8 km downstream. Participants express confusion about how to determine the optimum angle for the boat to reach the child, who is 0.6 km from the shore. Suggestions include labeling points in the diagram and using vector components to set up equations for the distances traveled by the boat. The conversation emphasizes the need to clarify the problem's requirements regarding the angle and whether it should be optimized.
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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