If an object is dropped from a height of 144 ft, the function h(t) = –16t² + 144 gives the height of the object after t seconds. When will the object hit the ground?
When the object hits the ground, the value of h(t) of the given function becomes 0 such that, 0 = -16t² + 144 or 144 - 16t² = 0 The equation above becomes a difference of two squares where 144 is the square of 12 and 16t² if the square of 4t. Factoring then gives, (12 - 4t) x (12 + 4t) = 0 12 - 4t = 0 ; t = 3 and 12 + 4t = 0 ; t = -3 The answer is 3 seconds.
