Solving Rainfall Velocity Problem with Vector Diagrams | 65 Chars

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The problem involves calculating the angle at which a man must hold his umbrella to stay dry while running in the rain. The rain falls at a velocity of 1 m/s, and the man runs at 5 m/s. A vector diagram was created to find the resultant velocity, which was determined to be approximately 5.1 m/s at an angle of 11.5 degrees. Another participant confirmed the calculation, providing a slightly different angle of 11.3 degrees. The discussion confirms the method and calculations used to solve the problem.
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Homework Statement


Rain is falling down with a velocity of 1m/s , perpendicular to the ground. A man runs with an umbrella with a velocity of 5 m/s.
Find the angle at which the umbrella must be held to ensure that the man remains dry.


I think i have solved this problem using the following diagram which i made.
the resultant vector is \sqrt{}26 m/s and \theta is approximately equal to 11.5o.

Could someone tell me if my answer is correct?


Thank you.
 

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Yes, it's correct, though I found the angle to be θ=11.3 degrees.
 
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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