# Kinematics question using vectors

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1. Nov 19, 2017

### Ofir12

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 :

3. 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.

Last edited: Nov 19, 2017
2. Nov 19, 2017

### haruspex

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?

3. Nov 19, 2017

### Ofir12

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 im wrong)

4. Nov 19, 2017

### Delta²

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 travelled $s_x$ and $s_y$ in each axis.