Vector addition. Please help.

[Aveym]

Haroon has a remote control electric toy boat that can travel at 6 m/s and wants to steer it across a 250 m wide river to his friend's dock. His friend's dock is on the opposite side of the river, 210 m downstream from looking straight across. There is a current of 2.5 m/s.
a) Draw a vector diagram for this situation and determine the heading that the boat should be steered at relative to the closest shoreline.
b) Determine the time it will take to cross the river.

 

[skeeter]

let [MATH]\theta[/MATH] be the angle the boat steers relative to the shoreline

[MATH]\Delta x = (6\cos{\theta} + 2.5) \cdot t = 210[/MATH]
[MATH]\Delta y = 6\sin{\theta} \cdot t = 250[/MATH]
Solve the system for [MATH]\theta[/MATH] and [MATH]t[/MATH].
I recommend you start by dividing the two equations, [MATH]\dfrac{\Delta x}{\Delta y}[/MATH], to eliminate the parameter [MATH]t[/MATH].

I hope you have a decent calculator ... you’re gonna need it.

 

[Deleted member 4993]

Haroon has a remote control electric toy boat that can travel at 6 m/s and wants to steer it across a 250 m wide river to his friend's dock. His friend's dock is on the opposite side of the river, 210 m downstream from looking straight across. There is a current of 2.5 m/s.
a) Draw a vector diagram for this situation and determine the heading that the boat should be steered at relative to the closest shoreline.
b) Determine the time it will take to cross the river.

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[Dr.Peterson]

Haroon has a remote control electric toy boat that can travel at 6 m/s and wants to steer it across a 250 m wide river to his friend's dock. His friend's dock is on the opposite side of the river, 210 m downstream from looking straight across. There is a current of 2.5 m/s.
a) Draw a vector diagram for this situation and determine the heading that the boat should be steered at relative to the closest shoreline.
b) Determine the time it will take to cross the river.

There are several ways to do this. You know the direction for the desired motion, and that the velocity vector for the boat, plus the vector for the current, must have that direction. You might use trigonometry, or components, or vector algebra. Once you show your own method (or at least tell us what you are learning), we can try to help you with it.

 

[Aveym]

Haroon has a remote control electric toy boat that can travel at 6 m/s and wants to steer it across a 250 m wide river to his friend's dock. His friend's dock is on the opposite side of the river, 210 m downstream from looking straight across. There is a current of 2.5 m/s.
a) Draw a vector diagram for this situation and determine the heading that the boat should be steered at relative to the closest shoreline.
b) Determine the time it will take to cross the river.
This is what I’ve done so far, can someone please tell me if its alright?

 

[Dr.Peterson]

Haroon has a remote control electric toy boat that can travel at 6 m/s and wants to steer it across a 250 m wide river to his friend's dock. His friend's dock is on the opposite side of the river, 210 m downstream from looking straight across. There is a current of 2.5 m/s.
a) Draw a vector diagram for this situation and determine the heading that the boat should be steered at relative to the closest shoreline.
b) Determine the time it will take to cross the river.
This is what I’ve done so far, can someone please tell me if its alright?
View attachment 23716

That's a very nice approach that I wouldn't have thought of. It amounts to using the Law of Sines on triangle BCD.

I would now check your answer by finding the components of each vector and confirming the vector sum.