# Thread: Projectile problem - finding the roots

1. ## Projectile problem - finding the roots

Hi,

I hope someone can help. I'm currently doing advanced functions, and I have been presented with a physics-related question that I don't know how to solve. I attached the question in this post:

I understand that I have to solve for t. In order to do that, I must know what the acceleration due to gravity is, the initial velocity, and the initial height. I know that the acceleration due to gravity is 3.92, and that the initial height is 1000. The only value that I don't know in order to solve for t is the initial velocity. Can anyone help?

BTW - the answer for this question is 22.59 seconds.

Best,
Olivia

2. ## Re: Projectile problem - finding the roots

The surface is at $s(t)=0~m$, The initial velocity is $v0=0~m/s$, the initial positions is $s0=1000~m$

$0 = -\dfrac{g t^2}{2} +0t +1000$

$\dfrac{g t^2}{2}=1000$

$t = \pm \sqrt{\dfrac{2000}{g}}$, and we can ignore the negative answer.

I leave you to plug $g$ in and punch the buttons.

3. ## Re: Projectile problem - finding the roots

Thank you! Makes sense.