Falling object and distance between time intervals

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SUMMARY

The distance a bowling ball falls from the Eiffel Tower can be calculated using the formula d=4.9t^2, where d represents distance in meters and t represents time in seconds. For the interval between the 8th and 9th seconds, the ball falls a distance of 50 meters, calculated by finding the distance fallen at 9 seconds (approximately 250 meters) and subtracting the distance fallen at 8 seconds (approximately 200 meters). If the calculated distance exceeds the height of the tower (324 meters), the ball would have hit the ground before the 9th second.

PREREQUISITES
  • Understanding of kinematic equations, specifically d=4.9t^2
  • Basic knowledge of gravitational acceleration (9.8 m/s²)
  • Ability to perform arithmetic operations with real numbers
  • Familiarity with the concept of free fall and its implications
NEXT STEPS
  • Study the implications of air resistance on falling objects
  • Learn about kinematic equations in physics
  • Explore the concept of terminal velocity and its effects on falling objects
  • Investigate real-world applications of gravitational physics in engineering
USEFUL FOR

Students studying physics, educators teaching kinematics, and anyone interested in understanding the principles of free fall and gravitational effects on objects.

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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)
 
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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.
 

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