While hovering near the top of a waterfall in a national park at

23042304
​feet, a helicopter pilot accidentally drops his sunglasses. The height
h left parenthesis t right parenthesish(t)
of the sunglasses after t seconds is given by the polynomial function
h left parenthesis t right parenthesis equals negative 16 t squared plus 2304h(t)=−16t2+2304.
When will the sunglasses hit the​ ground?

copy/paste of special symbols doesn't work too well here.

On the other hand, parentheses () and +-/* operators work just fine, as does the caret ^ for exponents, as in t^2.

Not sure how "​" appears to you, but it's gibberish on my screen.

To find when the sunglasses will hit the ground, we need to determine the time when the height (h(t)) is equal to zero.

Given that the height equation is h(t) = -16t^2 + 2304, we can set h(t) = 0 and solve for t:

0 = -16t^2 + 2304

To solve this quadratic equation, we can use the quadratic formula: t = (-b ± √(b^2 - 4ac)) / (2a), where our quadratic equation has the form ax^2 + bx + c = 0.

In this case, a = -16, b = 0, and c = 2304. Plugging these values into the quadratic formula, we have:

t = (0 ± √(0^2 - 4*(-16)*2304)) / (2*(-16))
t = (± √(0 - (-147456)) / (-32))
t = (± √(147456) / (-32))
t = ± (384 / -32)
t = ± (-12)

Since time cannot be negative in this context, we discard the negative solution.

Hence, the sunglasses will hit the ground when t = -12 seconds.