Finding Vector Magnitude & Direction in River Flow Problem

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To solve the river flow problem, the boat's velocity of 12 m/s across the river and the river's current of 6 m/s must be represented as vectors. Using the 'top and tail' method to draw these vectors helps visualize the resultant velocity as the hypotenuse of a right triangle formed by the two vectors. The magnitude of the resultant velocity can be calculated using the Pythagorean theorem, while the direction can be determined using trigonometric functions. This approach simplifies the problem, making it easier to understand the relationship between the boat's velocity and the river's flow. Ultimately, the discussion emphasizes the importance of visualizing vector problems to find both magnitude and direction effectively.
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This problem I'm not sure where to begin so if someone could just give me a hint...

A boat heads directly across a river with a velocity of 12m/s. If the river flows at 6.0m/s find the magnitude and direction (with respect to the shore) if the boat's resultant velocity.

I'm not sure how to find what way the direction is going without some kind of direction that is already given.
 
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Try actually drawing the vectors out 'top and tail' method. In this case the resultant force would be the hypotenues of the triangle formed. Therefore, the magnitude of the resultant force would simply be the magnitude or length of the hypotenues and the direction is easily found using trig.
 
thanks:) I think that I get this stuff now. I was making it harder than it had to be
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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