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I did the full working out for the following question (images attached below) but I don't know how to explain that the final answer is angles between the two angles 79.3 and 43.7 I've found. (The reason why I know this is the correct answer is because I have looked at the solution, I actually vaguely understand why lol) Could someone please explain to me why the answer is like that and what should i write at the end to validate my answer? Also is it always the case that the range of angles is always between the two angles I can find using the same tactic like above? Thank you so much for your help! enter image description here enter image description here

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Here is the answer handwritten by my teacher enter image description here

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[![enter image description here][5]][5]

BooScout
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    These are the two possibility for the angle. You either hit the target directly (while the projectile is still going Up) or you hit it while the projectile is going down. – Alain Remillard Apr 17 '20 at 23:35
  • @AlainRemillard Hi, thank you for your interest in my post. The thing that I don't really understand is that the answer is 43.7<the angle<79.3. I don't know how they deduce that after getting the angles. Does it also work that way? Getting two values for angle then the answer is between those angles? – BooScout Apr 17 '20 at 23:42
  • Could you add the complete answer? We have the diagram and your solution, but we don't have the question. – Alain Remillard Apr 17 '20 at 23:45
  • @AlainRemillard Hi I just provided the answer. I don't have the full working out solution, I only have a one-line answer handwritten by my teacher. Thank you! – BooScout Apr 17 '20 at 23:53
  • Sorry, I meant the question. Could you add the question? – Alain Remillard Apr 17 '20 at 23:55
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    @BooScout Alain Remillard is right: we need the question. The diagram from the question is not enough; we need to know what it is you're actually trying to calculate. For example, are you trying to hit the building? Launch over the building? What is happening here? – user771918 Apr 18 '20 at 00:34
  • @AlainRemillard Hi sorry for the lack of clarification before, I just editted the post. Thank you for helping me – BooScout Apr 18 '20 at 03:13
  • @user771918 Hi just editted the post. Thank you for your interest in the post. – BooScout Apr 18 '20 at 03:13
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    To land on the roof, the necessary condition is by the time the ball moves 20m horizontally, it is still at the air at a height $\color{red}{\ge}$ 15m. If the angle is $43.7^\circ$ or $79.3^\circ$, the ball hit the root at the front. For angles in between, the ball is still above the root at the 20m mark. If the roof extend indefinitely to the right, the ball will utimately land on the roof somewhere on the right. – achille hui Apr 18 '20 at 03:23
  • To really answer this question, it should have mention the width of the building. – Alain Remillard Apr 18 '20 at 11:59
  • @achillehui Hi, I got a vague idea of what's really going on here but I still don't understand that as the angle becomes greater, since we have H=(v^2sin(theta)^2/2g) (max height), the max height will become greater which means that as the angle becomes greater, it is more guaranteed that the at the range of 20m, the height is more than 50. So why is the angle being restricted up to 79 degrees here? Thank you for helping me! – BooScout Apr 22 '20 at 06:18
  • @BooScout if you throw a ball directly upwards, it will come down and hit your head ;-p When the angle is close enough to $90^\circ$, the ball cannot travel $20m$ before it hits the ground... – achille hui Apr 22 '20 at 07:20

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The crash between a ball and a building

Sometimes a picture worth more than thousand words in explanatory power.

Above picture illustrates what happens when you throw a ball towards the building.

  • When $4^\circ \le \theta \le 43^\circ$ (the red trajectories), the ball hit the front face of the building.
  • When $44^\circ \le \theta \le 79^\circ$ (the green trajectories), the ball fly over the top of the roof. It will either land on top of the roof or behind the building.
  • When $80^\circ \le \theta$ (the blue trajectories), the ball doesn't haven't enough time to travel horizontally before it either hit the ground or front face of building (when $\theta \sim 80^\circ$).

All of these is embedded in the math you have worked out, you just need to visualize the trajectories of the ball at different throwing angles.

achille hui
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