What is the acceleration due to gravity as measured in the following case and the time taken to fall from a height of 10 m in the following case:

An experiment is conducted to determine the acceleration due to gravity. A ball is dropped from a height of 1 m above the floor and the time taken to strike the floor measured as 0.45 s. How can the acceleration due to gravity be determined and what it is. Using the same value what would be the time taken by a ball to travel down from a height of 10 m.

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To measure the acceleration due to gravity the ball is dropped from a height of 1 m and the time it takes to strike the ground is measured as 0.45 s.

The acceleration due to gravity can be estimated using the relation s = u*t + (1/2)*a*t^2 where s is the distance traveled in t seconds by an object that starts at a velocity u and which is accelerated at a m/s^2.

Substituting the values: 1 = 0*t + (1/2)*g*(0.45)^2

=> g = 800/81 = 9.876 m/s^2

Using this value of acceleration due to gravity an object dropped from a height of 10 m would take a time t to strike the ground where 10 = 0*t + (1/2)(800/81)*t^2. This gives t^2 = 1620/800 and t = 1.423 s

The acceleration due to gravity is estimated to be 9.876 m/s^2 and the time taken to fall from 10 m is 1.423 s

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