Kinematics

[victorias]

In the solutions, they use the conservation of energy equation to solve this.
I am wondering why can't we use the big 5 equations here?

At the top, v2y = 0, can't we use v2 = v1 + 2ad ??

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[aldol16]

You can use any equation you want as long as you use it appropriately. You will get the same answer each time. Conservation of energy is just the easiest and quickest way. You know that all of the ball's initial kinetic energy has been converted to potential energy at 20 m and it's a simple square root from there to solve.

 

[theonlytycrane]

I believe so. Is the initial velocity = 20 m/s?

Edit: Didn't see @aldol16 's post above before posting. Either way works.

 

[aldol16]

I believe so. Is the initial velocity = 20 m/s?

Yes, it's 20 m/s.

Method 1: Conservation of energy

-m*g*h = 0.5*m*v^2
-2*g*h = v^2
v = sqrt(-2*-10*20) = sqrt(400) = 20 m/s

Method 2:

vf^2 = v0^2 + 2*g*h
0 = v0^2 + 2*g*h
v0^2 = -2*g*h

Same as above!

 

[NextStepTutor_3]

That's the awesome thing about kinematics - most equations are derived from conservation of energy (for example, v = sqrt(2gh)). So if you plug in the proper terms, you should always get the same answer.

The AAMC in particular really likes conservation of energy, though (which makes sense). So lots of problems can be solved faster that way than by scrambling to not only remember, but also choose the relevant one of the big 5 equations you mentioned. No matter what you do, though, always keep in mind what component (vertical or horizontal) you're dealing with. This question isn't too bad because the ball was kicked vertically, but if it were kicked at an angle, you'd have to keep in mind that it still has horizontal velocity at the top.

Anyway, good question!