Question

Please help!!!!! idk how to do this

Answer 1

Answer:

30 seconds.

Step-by-step explanation:

So, we have the equation:

$h(t)=-16t^2+h$

Where t is the time in seconds and h is the initial height.

A barometer falls from a weather balloon at a height of 14,400 feet. In other words, the initial height is 14,400. Substitute for h:

$h(t)=-16t^2+14400$

We need to find when the barometer hits the ground. Ground level is 0 feet. Therefore, we can substitute h(t) for 0 and solve for the equation (solve for t) in order to find how long (in seconds) it took for the barometer to fall:

$0=-16t^2+14400\\-14400=-16t^2\\900=t^2\\t=\pm\sqrt{900} \\\text{Time cannot be negative.}\\t=\sqrt{900}\\ t=30 \text{ seconds}$

Therefore, it took 30 seconds for the barometer to hit the ground when it fell at a height of 14,400 feet.

Edit: Spelling.