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A pebble drops from a balcony that is 80 feet above the ground. The pebble lands on the top of a sign that is 16 feet high. The function y=80−16t2 represents the height y (in feet) of the pebble t seconds after dropping from the balcony. How many seconds does the pebble drop before hitting the sign?

The pebble hits the sign after ______ seconds.

Respuesta :

Answer:

t =2 seconds

Step-by-step explanation:

We have, a function that represents the height y of the pebble after dropping the balcony as follows :

[tex]y=80-16t^2[/tex]

The pebble lands on the top of a sign that is 16 feet high.

It is required to find the time does the pebble drop before hitting the sign. The above equation becomes,

[tex]80-16t^2=16\\\\-16t^2+80=16\\\\-16t^2=64\\\\t^2=4\\\\t=2[/tex]

So, the pebble hits the sign after 2 seconds.

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