- #1
bolzano95
- 89
- 7
- Homework Statement
- Under what angle do we have to kick a ball up the hill so it comes back after n-rebounds?
- Relevant Equations
- α=?
I decided to try and find a solution in a green (tilted) coordinate system.
I started solving this problem with thinking about 1-rebound:
##⟹y=0, α=\text{angle under which we kick a ball}##;
##y=sin\alpha v_0t-\frac{1}{2}gt^2##; because I'm trying to solve this in a tilted system, I have to switch to ##g \implies a_y= gcos\varphi##. I get
## 0=sin\alpha v_0t-\frac{1}{2}gcos\varphi t^2##
##\frac{1}{2}gcos\varphi t^2=sin\alpha v_0t##
##\frac{1}{2}gcos\varphi t^2=sin\alpha v_0t \implies sin\alpha = \frac{cos\varphi}{2v_0}tg##
Here I got an angle under which I have to kick a ball for 1-rebound.
But which condition (or more of them) will give me an angle for n-rebounds?
I have been banging my head up the wall for the last few hours, even a relaxing break doesn't help anymore.
Thank you for your help.
I started solving this problem with thinking about 1-rebound:
##⟹y=0, α=\text{angle under which we kick a ball}##;
##y=sin\alpha v_0t-\frac{1}{2}gt^2##; because I'm trying to solve this in a tilted system, I have to switch to ##g \implies a_y= gcos\varphi##. I get
## 0=sin\alpha v_0t-\frac{1}{2}gcos\varphi t^2##
##\frac{1}{2}gcos\varphi t^2=sin\alpha v_0t##
##\frac{1}{2}gcos\varphi t^2=sin\alpha v_0t \implies sin\alpha = \frac{cos\varphi}{2v_0}tg##
Here I got an angle under which I have to kick a ball for 1-rebound.
But which condition (or more of them) will give me an angle for n-rebounds?
I have been banging my head up the wall for the last few hours, even a relaxing break doesn't help anymore.
Thank you for your help.
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