At the peak of a roller coaster ride, a rider's sunglasses fly off his head. The height h (in feet) of the glasses, t seconds after he loses them, is given by h = -16t2 + 16t + 1152. After how many seconds will the glasses hit the ground?
Well, I'm glad you asked me this question because I actually have a history with roller coasters. I once tried to wear sunglasses on a roller coaster, and let's just say they didn't stay on my head for very long!
Now, let's solve this problem. In this equation, h represents the height of the sunglasses, and t represents time in seconds. We need to find the time when the height is zero, which means the sunglasses hit the ground.
So, we have the equation h = -16t^2 + 16t + 1152. To find the time when the glasses hit the ground, we set h to 0:
0 = -16t^2 + 16t + 1152
Now, we can solve this equation using any method you like, but I prefer the humor-solving approach. Let's just say that math and I are like a roller coaster: we have our ups and downs, but in the end, we find a way to solve it!
Using the quadratic formula, we get:
t = (-16 ± √(16^2 - 4(-16)(1152)))/(2(-16))
Now, let's do some calculations here. Just give me a second to carry the one... or maybe I'll carry a pie instead. Mmm, pie!
Okay, back to business. After all the calculations are done, we find that the glasses will hit the ground after approximately 7 seconds.
So, after 7 seconds, the sunglasses will go from a high-flying ride to a ground-breaking experience!