Question

An acorn falls from the branch of a tree to the ground 25 feet below. The distance, S, that the acorn is from the

ground as it falls is represented by the equation S(t) = -16t² + 25, where t is the number of seconds. For which
interval of time is the acorn moving through the air?
0 0
○ 0 O
A
54

Answer 1

Explanation:

the acorn falls from the height of 25 feet above the ground, it means the initial time when it falls is t = 0. The time when it lands on the ground is t = 1.25

So the acorn was in the air for 1.25 seconds

Answer 2

The acorn is moving through the air during the interval 0 < t <= 5/4.

To determine the interval of time during which the acorn is moving through the air, we need to find when the distance of the acorn from the ground, S(t), is greater than 0.

Since S(t) = -16t² + 25, we set the equation equal to 0 and solve for t:

-16t² + 25 > 0

Using the quadratic formula, we find two time intervals:

t > 5/4 or t < -5/4

However, we are only interested in the time during which the acorn is falling, so we consider the interval 0 < t <= 5/4.

Therefore, the acorn is moving through the air during the interval 0 < t <= 5/4.