Question

I'm just not sure which approach I should take with this. I've tried applying a few equations (below) and none of them (from what i'm seeing) have the information needed to solve for a single variable.

"A frisbee is lodged in a tree branch 6.2 meters above the ground. A rock thrown from below must be going at least 3.0 m/s to dislodge the frisbee.

How fast must such a rock be thrown upward if it leaves the thrower's hand 1.1 meters above the ground?"

Answer 1

Equations:\[v = v _{o}+at\]\[x=x _{o}+vt+\frac{ 1 }{ 2 }at ^{2}\]\[v ^{2}=v _{o} ^{2}+2ax\]

Answer 2

So the rock travels a distance of
x = 6.2 - 1.1 = 5.1 m
before hitting the frisbee.

You know when the does hit the frisbee it must be travelling at v = 3.0 m/s

You want to find v_0

Answer 3

You need to fill in the blank with one more fact and then you can use one of these equations.

Answer 4

Following?

Answer 5

Yes, sorry, wasn't on earlier. I'll look at what you said, but I was just checking in this minute to see if I got a reply. Thanks!

Answer 6

Or I might have enough time now? Time will tell, no pun intended. I did the same thing you just did (equate the frisbee with 5.1 m) and from there can assume x (naught) = 0. From there, I can find that:\[5.1 = 0 + vt +\frac{ 1 }{ 2 }at ^{2}\]aaand i've got to go right now. I think my actual problem is the way i'm interpreting how it was written, e.g. "must be going at least 3 m/s". bbl.

Answer 7

I have give you x and v

You also know a. (Remember gravity?)
And you want to find v_0


Which equation has x, a, v and v_0? Use it!

Answer 8

Yeah, it was just an issue with the wording.\[v ^{2}=v _{o}^{2} + 2ax\]Given:\[9=v _{o}^{2}+2(-9.8)(5.1)\]Wait, what? Can't get a nonreal answer (negative square root). Is this just a reference frame problem, i.e. should a really just be |g|?

Answer 9

This doesn't imply \( v_0^2 \) is negative ...

Answer 10

I'm aware of that, but you can't take the square root of a negative number...? I understand what's implied. That doesn't mean that I can't question why it doesn't mesh with the math.

Answer 11

(Or, you can't get a real answer with a negative square root, which this definitely has to be.)