# TBR Physics I - Page 25

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#### bluishgreen

##### Full Member
7+ Year Member

I am mind fkd after seeing this equation(after paragraph 2) change so many times. And the second paragraph doesn't make any sense to me. can someone please explain it?

#### Catburr

##### Full Member
7+ Year Member
Can you be more specific about what confuses you? It's ok to quote the books.

The paragraph (at least in my book, with the blue cover, 2009 edition that I bought late last year) is about applying algebra to factor out time in the translational motion equation y = (initial velocity)(time) + (1/2)at^2.

Algebra, and the logic that y = 0 when the ball is on the ground.

#### bluishgreen

##### Full Member
7+ Year Member
The question which asks to find T_f_. I don't get it because it says to use equation 1.18 &#8710;y=v_oy &#8710;t+1/2 a_y (&#8710;t^2) . And how the heck does this equation change from this to t=2v_o/g ? I feel like this paragraph is all riddled up.

#### Blaughable

##### Full Member
10+ Year Member
So the question is asking when will the ball return back to the ground. Well that is when will the ball be at y=0.

Using Yf = Yo + Vot + 1/2at^2
where Yo=0, Yf=0

we get the equation:
0 = Vot + 1/2at^2

You can factor a t out of the right side and get:
0 = t(Vo+1/2at)

this equation can be true when either t=0 (before it is launched) or when what is inside the bracket equals 0:

Vo+1/2at = 0
t = -2Vo/a (a = -g)
t = 2Vo/g

#### bluishgreen

##### Full Member
7+ Year Member
this equation can be true when either t=0 (before it is launched) or when what is inside the bracket equals 0:

Vo+1/2at = 0
t = -2Vo/a (a = -g)
t = 2Vo/g

I don't get this. Can you please explain the math used here?

#### Blaughable

##### Full Member
10+ Year Member
I don't get this. Can you please explain the math used here?

NO problem:
Vo + 1/2at = 0

1.) Subtract Vo from both sides
(Vo + 1/2at)-Vo = 0-Vo
1/2at = -Vo

2.)Multiply by 2
2*(1/2at) = 2*(-Vo)
at = -2Vo

3.) divide by acceleration
(at)/a = (-2Vo)/a
t = -2Vo/a

#### bluishgreen

##### Full Member
7+ Year Member
thanks soooo much.