Final answer:
After 6 seconds, the rocket would have fallen 579.6 feet due to gravity if it were not interrupted by hitting the ground. However, since the building is only 500 feet tall, the rocket would hit the ground before 6 seconds have passed.
Step-by-step explanation:
The student's question relates to the motion of a rocket that is dropped from a height and how far it will fall within a certain time frame due to gravity. When an object is dropped, it accelerates downwards under the influence of gravity, which on Earth has a value of 9.8 m/s² (approximately 32.2 ft/s²). To calculate the distance the rocket will have fallen after 6 seconds, we can use the kinematic equation for gravity-driven free fall without initial velocity:
d = 0.5 * g * t²
Where:
- d is the distance fallen
- g is the acceleration due to gravity (32.2 ft/s²)
- t is the time in seconds
So, for 6 seconds:
d = 0.5 * 32.2 ft/s² * (6 s)²
d = 0.5 * 32.2 * 36
d = 579.6 feet
The rocket will have fallen 579.6 feet after 6 seconds, but given that the building is only 500 feet tall, the rocket will have hit the ground before the 6 seconds are up. Therefore, it will not fall 579.6 feet through the air; instead, it will hit the ground at some point before reaching this distance.