What is the height when the object has half its initial velocity?

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To find the height at which a ball has half its initial velocity, given a maximum height of 37 m and an initial velocity of 26.9 m/s, the kinematics equation can be applied. The initial velocity is halved to 13.45 m/s. The discussion clarifies the focus is on determining the elevation when the object reaches this half-velocity, rather than the time or velocity at a specific height. The necessary calculations involve using the kinematic equations to solve for height at this velocity. The goal is to accurately identify the elevation corresponding to half of the initial velocity.
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I am instructed in a question to find half of the initial velocity if the max. height of a ball going upward is 37 m. I believe I have found the initial velocity to be 26.9 m/s - so I'm thinking the rest should be simple, right?

For instance if I took the kinematics equation v = v_0 + at, I should be able to rearrange and solve for half of v_0, correct? Or something...?

Thanks!

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Morgan
 
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Huh?
If v_o = 26.9 [m/s] , half of v_o = 13.45 [m/s] .

Did you want to find the *time* when v = 1/2 v_o ,
or the elevation where the object has 1/2 v_o ?
Did you want to find the velocity at half the 37 [m] ,
or the elevation at half the rise time?
 
Sorry... I'm looking for the height (elevation) when the object has 1/2 its initial velocity... does that clarify?
 
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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