Question

The function h(t) = -16x t² + 400 represents the height, in feet, of an object from the ground at t seconds after it is dropped. Determine how far the object falls between 2 and 3 seconds.

A. 90 feet
B. 50 feet
C. 80 feet
D. 65 feet

Answer 1

The object falls 80 feet between 2 and 3 seconds after being dropped, as calculated by evaluating the height function at 2 and 3 seconds and finding the difference between the two heights.

Step-by-step explanation:

To determine how far the object falls between 2 and 3 seconds, we need to calculate the height of the object at 2 seconds and 3 seconds, then find the difference between the two. The function h(t) = -16t² + 400 gives the height of an object from the ground at t seconds after it is dropped, where t is the time in seconds and h(t) is the height in feet.

First, find h(2):

h(2) = -16(2)² + 400 = -16(4) + 400 = -64 + 400 = 336 feet

Then, find h(3):

h(3) = -16(3)² + 400 = -16(9) + 400 = -144 + 400 = 256 feet

To find the distance the object falls between 2 and 3 seconds, subtract the height at 2 seconds from the height at 3 seconds:

Distance fallen = h(2) - h(3) = 336 feet - 256 feet = 80 feet

The object falls 80 feet between 2 and 3 seconds.