# Determining speed of an object with only a meter stick?

#### fattydq

A child wishes to determine the speed a slingshot imparts to a rock. How can this be done using only a meter stick, a rock, and the slingshot?

This question seems impossible to me, since you would HAVE to take time into account at some point, in some way, to figure out speed, right? So is this a trick question or am I missing something?

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#### RoyalCat

Think ballistics. :)

I'll help you get started:
$$y(x)=tan{\theta}\cdot x-\frac{g}{2v_0^2cos^2{\theta}}\cdot x^2$$

Where $$\theta$$ is the angle the initial velocity of the projectile makes with the horizon.

#### fattydq

Yes, but figuring out the angle would require more than just the meter stick, rock, and sling shot, wouldn't it?

#### RoyalCat

Yes, but figuring out the angle would require more than just the meter stick, rock, and sling shot, wouldn't it?
I don't know about you, but I'm pretty good at making a 45° angle. :P

#### fattydq

Haha, yeah, that's what's throwing me about this problem though...the fact that you can ONLY use those materials. That's why I think it may be a trick question or something haha.

#### OmCheeto

Gold Member
Haha, yeah, that's what's throwing me about this problem though...the fact that you can ONLY use those materials. That's why I think it may be a trick question or something haha.
I don't think it's a trick question. If you drop the rock from one meter above the ground then the distance traveled by the rock will be zero. Shooting the rock horizontally from the one meter height with the slingshot will send the rock a certain distance before it hits the ground. The higher the speed of the rock, the further it will go, which can be measured with the yard stick.

You then figure out the time, based on how long it takes a rock to fall from one meter height.
Since speed is just distance over time, you'll have your answer.

#### fattydq

And that time would just be a constant right? The constant of gravity, that is?

#### OmCheeto

Gold Member
And that time would just be a constant right?
In the context of this problem, yes.
The constant of gravity, that is?
Gravity is a constant, but dropping something from a two meter height will yield a different time constant.

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