Catching a Ball Thrown at 30 m/s: Solving the Physics Problem

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A ball is thrown straight up at 30 m/s, and a person 70 m away needs to run to catch it before it lands. The initial calculations suggested a time of 6.99 seconds and a running speed of 10.00 m/s, but this was found to be incorrect. The correct time to reach the ball was recalculated to be 6.12 seconds using the equation s = ut + 1/2 at². Clarification was needed regarding the variable 'u,' which represents the initial velocity. The discussion highlights the importance of correctly applying physics formulas and conventions for accurate problem-solving.
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A ball is thrown straight up in the air at an initial speed of 30 m/s. At the same time the ball is thrown, a person standing 70 m away begins to run toward the spot where the ball will land.

How fast will the person have to run to catch the ball just before it hits the ground?

Ok, I have used the quadratic formula to come up with my Time (6.99 seconds) and then divided it into 70m, and came up with 10.00m/s for the V of the person. This is incorrect per my physics book.

I'm thinking the problem occurred on the -x part of this equation:

http://physics.webplasma.com/image/page05/kin07.gif

I put 0, since the ball didn't move anywhere - all it did was go up and down. Any ideas where my source of error occurred at? Thank you so much!
 
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I am assuming you started with the equation s = ut + \frac{1}{2}at^{2}, I solved this equation and found t to be equal to 6.12 seconds. You may want to check your arithmetic. Your method looks good to me. Nice presentation btw :smile:
 
hmm, you are correct. What is 'u' supposed to represent again? I thought I had these formulas down - apparently not.
 
mikefitz said:
hmm, you are correct. What is 'u' supposed to represent again? I thought I had these formulas down - apparently not.
u in my equation is equal to your v0 or initial velocity. Apologies for the confusion I should have stuck to your convention.
 
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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