Question on Physics problem of time and distance

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The discussion revolves around solving a physics problem involving a ball thrown from a 96-foot building with an initial velocity of 80 ft/s. The equation given for the distance traveled is d = 96 + 80t - 16t². The user needed to find the time it takes for the ball to reach the ground (d = 0) and the top of the building (d = 96). After applying the quadratic formula, the user determined that it takes 6 seconds to reach the ground and 5 seconds to reach the top of the building. The conversation also notes that there is a negative time solution, indicating a theoretical scenario where the ball would have been thrown from the ground.
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I have this problem I am doing for college algebra. Its been giving me a lot of trouble and i have know idea how to handle it. the problem is that is a ball that were thrown from the top of a 96 foot building traveling at an initial velocity of 80 ft/s would travel from there all the way to the ground how many seconds would it reach the ground(a) and the top of the building(b)? they also give an equation for that represents the distance traveled (d=96+80t-16t^2) I've been stuck on the problem for a good while and have now idea how to go by it
 
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Hi Daniol10! Welcome to PF! :smile:

(try using the X2 button just above the Reply box :wink:)

ok, so you have an equation d = 96 + 80t - 16t2,

and you need to sove it for (a) d = 0, and (b) d = 96.

sooo … just put that value of d into the equation, and solve it as an ordinary quadratic equation in t …

what do you get? :smile:​
 
Thanks! I had forgotten about the quadratic formula. I ended up with 6 sec for (a) and 5 sec for (b)
 
Fine! :smile:

btw, you'll notice that both equations have another solution …

eg for (a) it's -1 s, which is when it would have had to be thrown from the ground to follow the same trajectory! :wink:​
 
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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