How Does the Pilot's Speed Affect the Observed Falling Speed of a Package?

AI Thread Summary
The discussion centers on understanding how a pilot's speed affects the observed falling speed of a package. A stationary observer sees the package falling at speed v1 at an angle, while the pilot, flying horizontally, perceives the package falling vertically at speed v2. The key question is determining the pilot's speed relative to the ground. Participants are encouraged to visualize the situation by drawing velocity vectors for both the package and the pilot. The conversation emphasizes the importance of connecting these vectors to solve the problem effectively.
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1. At a particular instant, a stationary observer on the ground sees a package falling with speed v1 at an angle to the vertical. To a pilot flying horizontally at constant speed relative to the ground, the package appears to be falling vertically with a speed v2 at that instant.
WHAT IS THE SPEED OF THE PILOT RELATIVE TO THE GROUND.


2. Homework Equations
Pythagorean Theorem


The Attempt at a Solution


I have no idea how to draw this picture up. please help.
thanks
 
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draw the velocity vectors of the package and the pilot. the pilot sees the package as is it falls vertically - use that as a connection between their vectors.
 
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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