A brick is dropped from the Empire State Building at a height of 324 meters. If you neglect any type of air resistance, what is the distance in meters that the ball falls during the interval between the 8th and 9th second?

what is the distance at 9 meters?

what is the distance at 8 meters?
subtract the two.

d=1/2 g t^2

To find the distance the brick falls during the interval between the 8th and 9th second, we first need to calculate the time it takes for the brick to reach the ground.

The equation that relates the distance fallen (d) to time (t) under free fall with no air resistance is given by:
d = (1/2) * g * t^2,

where g is the acceleration due to gravity, which is approximately 9.8 m/s^2.

To calculate the time it takes for the brick to reach the ground from a height of 324 meters, we can rearrange the equation to solve for time:
t = sqrt(2d/g).

Plugging in the value for d (324 m) into the formula, we get:
t = sqrt(2 * 324 / 9.8).

Evaluating this expression, we find:
t ≈ 8.03 s (approximately).

Now, to find the distance fallen during the interval between the 8th and 9th second, we need to subtract the distance fallen in the first 8 seconds from the distance fallen in the first 9 seconds.

The distance fallen in the first 8 seconds can be calculated using the same formula, but plugging in the time of 8 seconds:
d_8 = (1/2) * g * t_8^2,
where t_8 = 8 seconds.

Similarly, the distance fallen in the first 9 seconds is:
d_9 = (1/2) * g * t_9^2,
where t_9 = 9 seconds.

Finally, the distance fallen during the interval between the 8th and 9th second is:
d_9 - d_8.

By substituting the values for d_8, d_9, and t_8, we can calculate the result:
d_8 = (1/2) * 9.8 * 8^2,
d_9 = (1/2) * 9.8 * 9^2,
result = d_9 - d_8.