Confusing word problem quadratic equations and problem solving

Question

An object is thrown upward from the top of a 64-foot building with an initial velocity of 48 feet per second. The height h of the object after t seconds is given by the quadratic equation h= -16t^2+48t+64. When will the object hit the ground?

Answer 1

The given equation governs the height versus time of the object. h(0) = 64, so the ground is considered at h = 0. The question is at what time is h = 0? So, set h = 0 and solve for t.

 

-16t^2 + 48t + 64 = 0

 

We can divide both sides of this equation by -16 for simpler numbers. We get

 

t^2 - 3t - 4 = 0

 

We can factor this equation:

 

(t - 4)(t + 1) = 0

 

So, t = 4 and t = -1 are solutions.

 

But, time must be positive, so t = -1 makes no sense, so we discard it. This leaves

 

t = 4 sec