Math Help - Distance between Ball thrown downwards and it's starting point?

1. Distance between Ball thrown downwards and it's starting point?

A tennis ball is thrown down from the top of a 120m building with an initial velocity of 8m/s. What is the distance of the ball from the top of the roof 2 seconds after it was thrown?
Acceleration due to gravity is 9.8m/s^2

Please don't use a physics formula to solve this question. Use derivatives.

Thank you so much!

2. You could start by saying

$a = -9.8 \implies v = \int a ~dt = v = \int -9.8 ~dt = -9.8t+c$

You are told your initial velocity is $v_0 = -8$ therefore
$v = -9.8t-8$

Now do the same to find the distance $x = \int v ~dt$

After you have this find $x(2)$