Question

A ball is dropped from a treetop 64 feet above the ground. How long does it take to hit the ground? (s = 16t 2) 1 second 2 seconds 3 seconds

Answer 1

A nice physics problem.

But 16t 2 is inappropriately written; you meant  x = 16t^2, where "^" represents exponentiation.

The appropriate formula applying to this situation includes a "t" term which is not present in yours.  Start with this:

s = s_0 + v_0t + (1/2)a^t^2, where x_0 is the initial height above the ground and v_0 is the initial velocity.  "a" represents acceleration an here is -32.2 ft/(sec^2).

Here's how we apply this formula:

0 ft = 64 ft + 0*t + (1/2)(-32.2 ft/(sec^2), or

0 ft = 64 ft - 16.1 ft/(sec^2)

You must solve this equation for time, t.  It will be a positive quantity.