Final answer:
It takes approximately 2.41 seconds for the acorn to fall 40 feet.
Step-by-step explanation:
In this problem, we can use the laws of physics to calculate the time it takes for the acorn to fall 40 feet. We can assume that the acorn is dropped from rest, so its initial velocity is zero. Using the equation for accelerated motion, we can find the time it takes for the acorn to fall using the equation:
d = \frac{1}{2}gt^{2}
where d is the distance, g is the acceleration due to gravity (approximately 32.2 feet per second squared), and t is the time. Rearranging the equation to solve for t, we get:
t = \sqrt{\frac{2d}{g}}
Substituting the given value of d as 40 feet and g as 32.2 feet per second squared, we can calculate the time it takes for the acorn to fall:
t = \sqrt{\frac{2 \cdot 40}{32.2}} = \sqrt{\frac{80}{32.2}} \approx 2.41 \text{ seconds}
Therefore, it takes approximately 2.41 seconds for the acorn to fall 40 feet.