When will the sunglasses hit the ground in this problem?

Question

While hovering near the top of a waterfall in a national park at 5184 feet, a helicopter pilot accidentally drops his sunglasses. The height h(t) of the sunglasses after t seconds is given by the polynomial function h(t)=-16t^2+5184. When will the sunglasses hit the ground?

Answer 1

Given the function h(t)=-16t²+5184, and you want to know when the glasses hit the ground, that means h=0.  Substitute this, and then solve for t.

 

0=-16t²+5184  [I wanted to use the quadratic formula, which must be in the form 0=ax²+bx+c, so I added 0t]

0=-16t²+0t+5184  [Next, I applied the quadratic formula]

t={-(0)+/-√[0²-(4)(-16)(5184)]}/[(2)(16)]

t=(0+/-576)/-32  [Since time cannot be negative, you can eliminate 0+576 as a possibility)

t=-576/-32

t=18

 

Therefore, the glasses will hit the ground in 18 seconds.