Question

The height h (in feet) of an object dropped from a window after x seconds can be modeled by h(x)=−16x2+64 . The object is dropped a second time so that it hits the ground 1.5 seconds sooner. Write a function g that models the path of the object the second time it is dropped.

Answer 1

g(x) = - 16x² + 4

Explanation:

Given the model:

First drop:

h(x) = - 16x² + 64

Second drop hits the ground 1.5 seconds sooner

Function g(x) to model the second drop:

-16t² + V0t + h0

h(x) = - 16x² + 64

0 = - 16x² + 64

16x² = 64

x² = 64/16

x = 2

1.5 seconds sooner :

X = 2 - 1. 5

x = 0.5

0 = - 16(0.5)² + 0 + h0

0 = - 4 + h0

h0 = 4

Hence,

g(x) = - 16x² + 4