What is the acceleration of a spacecraft during liftoff?

AI Thread Summary
To determine the acceleration of a spacecraft during liftoff, the problem states that it reaches an altitude of 450 meters in 4 seconds while uniformly accelerating from rest. The key equations of motion, which include displacement, velocity, and acceleration, are necessary to solve for acceleration. The user is uncertain about how to categorize altitude in terms of displacement and is seeking guidance on the relevant equations. Understanding that displacement is indeed the vertical distance traveled will help in applying the equations correctly. The discussion emphasizes the need for clarity on the relationship between displacement, time, and acceleration in this context.
elleleeanne
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Homework Statement



Within 4 sec of liftoff, a spacecraft that is uniformly accelerating straight upward from rest reaches an altitude of 450 m [up]. What is the spacecraft 's acceleration?

Homework Equations



The five key equations, plus the velocity, speed, and acceleration equations

The Attempt at a Solution



I don't know what the altitude would be (Displacement? Distance?), so I can't solve the equation with the five key equations.
 
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Do you know an equation from the key equations that involves displacement+velocty+time+acceleration?

Hint: displacement = ??
 
Thank you so much!
 
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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