Boat Passenger Velocity on Stairs in 2D Motion Problem

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To determine the velocity of a passenger walking up stairs on a moving boat, vector addition is necessary. The boat's velocity is 1.25 m/s, and the passenger's velocity relative to the boat is 0.50 m/s at a 45° angle. The total velocity of the passenger relative to the water is the sum of these two velocities. The problem requires calculating both the magnitude and direction of this resultant velocity. Understanding vector addition is crucial for solving this type of physics problem.
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Homework Statement


A passenger on a boat moving at 1.25 m/s on a still lake walks up a flight of stairs at a speed of 0.50 m/s, Fig. 3-44. The stairs are angled at 45° pointing in the direction of motion as shown. What is the velocity of the passenger relative to the water?

Magnitude = ___m/s
Direction= ___° (above the water)

Could someone please help me with this problem... I've been stuck on it all night, and can't seem to figure out the correct method of solving it... Help would be greatly appreciated... Thanks =)
 
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Not sure without the picture. But it seems like a vector addition problem. The velocity of the passenger wrt water, is the vector sum of:

the velocity of the boat wrt water + the velocity of the passenger wrt the boat.
 
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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