Falling object and distance between time intervals

[Jakedidit]

Homework Statement

Gravity on a falling object causes the object to descend a distance of d=4.9t^2, where d is the distance in meters and t is the time in seconds. A bowling bll is dropped from the top of the Eiffel Tower in Paris, France, which is 324 meters in height. 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?

Homework Equations

d=4.9t^2 is given;
Gravity acceleration is 9.8 m/s^2

The Attempt at a Solution

Should we calculate the distance the bowling ball will fall in 8 seconds? then 9 seconds? then subtract the two? (Can't fall more than 324 meters)

 

[calum]

Calculate how far it has fallen in 8 seconds. Then calculate how far it has fallen in 9 seconds.

If for example in 8 seconds it has fallen 200m and in 9 it has fallen 250m then the distance is 50m.

But if your distance at 9 seconds is over 324m then it will have hit the ball between the 8th and 9th second, so you will just take away the distance at the 8th second from 324.

 

[Architeuthis Dux]

Yes, that would be the correct approach. First, we can calculate the distance the ball falls in 8 seconds using the given equation d=4.9t^2, where t=8 seconds. This gives us a distance of d=313.6 meters. Then, we can calculate the distance the ball falls in 9 seconds using the same equation, but with t=9 seconds. This gives us a distance of d=441.9 meters.

To find the distance between the 8th and 9th second, we can subtract the distance at t=8 seconds from the distance at t=9 seconds. This gives us a distance of 441.9 - 313.6 = 128.3 meters. Therefore, the ball falls a distance of 128.3 meters during the interval between the 8th and 9th second.

It is important to note that this calculation assumes there is no air resistance, which may not be the case in real life. However, for the purpose of this problem, neglecting air resistance is a reasonable assumption.