# Thread: Solving limits with free fall

1. ## Solving limits with free fall

Hello,

Just started calculus. I am fairly comfortable with limit problems in what has been given to us, but I'm thoroughly lost when given a problem like this.

Any help would be appreciated, thanks.

2. ## Re: Solving limits with free fall

When you replace s(a) and s(t) with $\displaystyle -4.9a^2+200$ and $\displaystyle -4.9t^2+200$, you get a lot of cancellation. Remember the identity $\displaystyle x^2-y^2=(x+y)(x-y)$.

They're getting you ready for derivatives - the limit you are calculating is just the derivative of s(t) at a.

- Hollywood

3. ## Re: Solving limits with free fall

So s(a) and s(t) are the exact same? Why do they have different letters then?

4. ## Re: Solving limits with free fall

No, $\displaystyle s(a)=-4.9a^2+200$ and $\displaystyle s(t)=-4.9t^2+200$. So when you plug them in, 200 cancels and you can factor out -4.9, giving $\displaystyle \frac{a^2-t^2}{a-t}$.

- Hollywood