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A canon is fired Horizontal to the ground 80 meters above ground The canon ball is fired a $T=0$ and hits the ground at $T_g$. Calculate the height at the time $T_g/2$ So far I have calculated time. which gives me the equation $$y=y_i+v_{iy}(4.05) - (0.5)(9.82)(4.05^2)$$ Now my problem is that when I try to calculate $v_{iy}$ I am getting $-37\text{ m/s}$ which I know is not the case; it wouldn't make any sense. $Y$ initial is equal to $80\ \ V_{iy}$ I don't know $4.05$ is the time it takes the projectile to hit the ground. $9.82$ is gravity which is my acceleration.
So my question is two parts. First, is this the best equation to find what I'm trying to find? Second, how do I find velocity in the $y$ direction when $\theta$ is $180$ degrees? This is an edited question I do apologize for being unclear. Thank you for responding and requesting clarification. I was using the incorrect equation a simpler way to find the answer would be $y=.75\times H$. Because change in $y = -.5\times g\times t^2$ sense initial velocity in the $y$ direction equals $0$. Thank you for the help in structuring my question better.

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closed as off-topic by Brandon Enright, Kyle Kanos, Abhimanyu Pallavi Sudhir, Waffle's Crazy Peanut, Emilio Pisanty Mar 2 '14 at 5:01

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – Brandon Enright, Kyle Kanos, Abhimanyu Pallavi Sudhir, Waffle's Crazy Peanut, Emilio Pisanty
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Your question does not make sense as is. There isn't any diagram or context description, only a formula with numbers that popped out of nowhere, and the question that follows is unclear. Please edit your post with a clear description of the problem, what you have done so far in algebra then the numerical application, and a clear question. We can still guess and I'm going to answer but you should really pay attention to that or you'll have very little chance of having answers in the future. $\endgroup$ – Mister Mystère Mar 2 '14 at 0:51
  • $\begingroup$ I have updated what I have done so far I am not sure if this is what you wanted is there a chance you could point me in the direction of what you would consider a better asked questions so I can in the future ask a better question? If not could you tell me what else I am missing? $\endgroup$ – user41607 Mar 2 '14 at 1:03
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    $\begingroup$ Hello Mr./Ms. Moderator, I am unsure as to why this has been flagged, is there anyway I could be told more detail than the standard message about something being off topic Also as I wanted to be guided wasn't looking for an answer but an equation I do not see how I am breaking any of your stated rules. At this point I have asked several question all of which have been answered to my satisfaction even though one was edited by me and another was edited by someone else, I am afraid all of my questions break this unknown rule. $\endgroup$ – user41607 Mar 2 '14 at 5:59
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    $\begingroup$ In addition I would like to refute each point in specific so if anyone does respond they can show me exactly wher eI am Misunderstanding the rules: Ask about a specific physics concept: I asked about horizontal projectile equation I figure thats fairly specific. Show some effort to work through the problem: I showed what I had done so far had already solved for one variable and explained my understanding about the remaining variable and what I had gotten so far for it. $\endgroup$ – user41607 Mar 2 '14 at 6:34
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    $\begingroup$ Useful to the broader community: Considering this is on both my midterm and final as a concept as well as being on many questions with in my homework I think I can safely assume any answer would be useful to someone else at my level of understanding of physics, unless of course I asked a question too far below the intelligence of the community in which case i apologize for asking questions here I will gladly move to another forum that allows freshman college level questions. $\endgroup$ – user41607 Mar 2 '14 at 6:35
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[Edit: If you don't consider air friction and if you're not asked anything about the range of the projectile, the equations are the same as a vertical freefall]. If you are trying to find the velocity of the object at any given time, it is not $v_{iy}$ that you need to calculate since it is the initial velocity of the object at $t=0$.

Step by step for a vertical freefall (1D) with origin on the ground at the vertical of the initial position of the object and y axis toward the object: $$-g=a_y$$ $$\Rightarrow v(t) = \int^t_0 -g.dt=-g.t+v_{0y}$$ $$\Rightarrow y(t) = \int^t_0 (-g.t+v_{0y}).dt=-\frac{1}{2}g.t^2+v_{0y}.t+y_0$$ Here $v_{0y}$ is 0 and $y_0=80m$. You're interested in $v(T_g/2)$ where $T_g$ is $t$ so that $y(t)=0$.

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  • $\begingroup$ Not quite I apologize for not defining I am not trying to find the height of an object in free fall but the height of an object halfway to the ground that has been fired from a cliff of 80 meters high and fired parallel to the ground. $\endgroup$ – user41607 Mar 2 '14 at 1:06
  • $\begingroup$ If you don't have any questions about the range of the projectile or anything, you only need the y axis. This is considering that there isn't any air friction, of course, and that is why you haven't been given the initial horizontal velocity. Plug in $y_0$ in y(t) to solve for t, which you have done, then plug that t (named $T_g$ apparently) in v(t). Done. $\endgroup$ – Mister Mystère Mar 2 '14 at 1:17
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    $\begingroup$ Thank you I was over complicating it. This is an awesome answer It's nice to get it step by step. Thank you. $\endgroup$ – user41607 Mar 2 '14 at 1:28

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