Can you help me with this algebra equation

Question

A pebble drops from a balcony that is 160 feet above the ground. The pebble lands on the top of a sign that is 16 feet high.  The function  represents the height  (in feet) of the pebble  seconds after dropping from the balcony. How many seconds does the pebble drop before hitting the sign?

Answer 1

Hi Steve. So it seems that your function didn't load, but assuming the question follows generic physics, the function should be that of any object in free fall:

d = 1/2 at²

where d = distance (or height in this case), a = acceleration (gravity, 32.2 ft/s²), and t = time

Now let's rearrange our function.

2d = at²

(2d / a) = t²

√(2d / a) = t

Now let's plug in our terms

t = √(2 * (160-16) / 32.2)

Follow your order of operations,

t = √(2 * (144) / 32.2)

t = √(288 / 32.2)

t = √(8.944)

t = 2.99s

And that is your answer. Respond to let us know if that was indeed your function. If not, I'm sure we can help further.

Answer 2

Usually the function involved would be h(t) = h(0) - 16t²

^and

16 = 160 - 16t²

16t² = 166 => t² = 9 and t = 3

Answer 3

Answer 4