Sol'n: Law of Cosines - Find Direction to Return After Walking 220m, 50m

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To determine the return direction after walking 220 m west and then 50 m at a 45-degree angle towards north, the Law of Cosines is applied to find the length of the return path. The angle used in the calculation is 135 degrees. To find the direction for the return trip, the Sine Rule is suggested to calculate the necessary angle. This method allows for determining both the distance and the precise direction needed to return to the starting point. Understanding these concepts is crucial for solving the problem effectively.
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Homework Statement



You walk 220.0 m due west, then turn 45.00 degrees toward north and walk another 50.00 m. how far and in what direction do you need to walk to get back to where you started?

Homework Equations


Law of Cosines


The Attempt at a Solution



I did the law of cosines to find the lenngth of side c. I used the angle measure of 135 degrees. I am not sure how to find the direction though. What degree is it?
 
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Welcome to PF!

panthergk said:
I did the law of cosines to find the lenngth of side c. I used the angle measure of 135 degrees. I am not sure how to find the direction though. What degree is it?

Hi panthergk! Welcome to PF! :smile:

YOu now have one angle and all three sides, and you want another angle …

so use the sine rule. :wink:
 
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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