Question

This is an emergency. I need assistance.

1: The distance, d, that an object falls is directly proportional to the square of the time, t, it has been in free fall. An object that has been in free fall for 8 seconds has fallen 1024 feet. Determine the distance the object has fallen if it has been falling for 3 seconds.
2: The distance, d, that an object falls is directly proportional to the square of the time, t, it has been in free fall. An object that has been in free fall for 8 seconds has fallen 1024 feet. Determine the distance the object has fallen if it has been falling for 2 seconds.
A) 144 feet, 64 feet
B) 196 feet, 100 feet
C) 64 feet, 144 feet
D) 100 feet, 196 feet

Answer 1

The distances an object in free fall has traveled after 3 and 2 seconds are 144 feet and 64 feet respectively, when the initial distance at 8 seconds is 1024 feet. The correct answer is A) 144 feet, 64 feet.

Step-by-step explanation:

Given that the distance d an object falls is directly proportional to the square of the time t it has been in free fall, an object that has fallen for 8 seconds has traveled 1024 feet. We can set up a proportionality relationship to find the constant of proportionality k: d = k × t2. Using the given information, we can find k as follows: 1024 feet = k × 82, so k = 1024 / 64 = 16.

To determine the distance after 3 seconds, we apply the formula d = 16 × 32 = 16 × 9 = 144 feet. And for 2 seconds, d = 16 × 22 = 16 × 4 = 64 feet. So the distances the object has fallen after 3 and 2 seconds are 144 feet and 64 feet respectively.

Therefore, the correct answer is A) 144 feet, 64 feet.