/sci/ - Science & Math

[Anonymous No.7067653]

I normally wouldn't ask this here but this shit is pissing me off. The answer is supposed to be of the form R = a(H^b)(h^c). With a, b, and c being constants. I can't figure out what I'm doing wrong.

[Anonymous No.7067672]

>>7067653
What I did is fairly self-explanatory, so here it goes: <div class="math">\frac{1}{2} g t_{H\to h}^2 = H-h \Longrightarrow t_{H\to h} = \sqrt{\frac{2(H-h)}{g}}</div> <div class="math">\frac{1}{2} g t_{h\to 0}^2 = h \Longrightarrow t_{h\to 0} = \sqrt{\frac{2h}{g}}</div> <div class="math">v_{0x} = gt_{H\to h} = \sqrt{2 g (H-h)}</div> <div class="math">R = v_{0x}t_{h\to 0} = 2\sqrt{h(H-h)}</div> So I basically don't have anything of the form <span class="math">R = a(H^b)(h^c)[/spoiler], but that could be due to a misunderstanding regarding the definition of H, h.

[Anonymous No.7067677]

>>7067653
I haven't done this shit in ages but I get
2(H^1/2)(h^1/2)

[Anonymous No.7067679]

>>7067653
Oh I didn't realise that's also what you got... Are you sure it's wrong?

[Anonymous No.7067680]

>>7067653
t=√(2h/g)
vx=√(2(H-h)g)
x=2√(h(H-h))

Sanity checks:
H=h -> x=0
h=0 -> x=0
units √(m^2)=m

[Anonymous No.7067685]

>Ball is dropped from height H
>Total height is H+h