Question

An object is dropped out of a window of a building. The function h (t) = −16t² + 36 models the height, h (t), in feet, of the object above the ground t seconds after it is dropped.

What is the best description of the meaning of h (1.5) = 0 in terms of the context?

a. the object is dropped from an initial height of 1.5 feet
b. the object travels at a speed of 1.5 feet per second after it is dropped
c. the speed of the object increases at a rate of 1.5 feet per second each second after it is dropped
d. the object hits the ground 1.5 seconds after it is dropped​

Answer 1

The correct answer is d.

The equation h(t) = -16t^2 + 36 gives the height of the object above the ground at time t. So, h(1.5) gives the height of the object 1.5 seconds after it is dropped. If h(1.5) = 0, it means the height of the object is zero, or it has hit the ground at that time. Therefore, the best description of the meaning of h(1.5) = 0 in terms of the context is that the object hits the ground 1.5 seconds after it is dropped.