Seed Question 71

A ball falls freely from rest at a height of 2 meters. Observations indicate that the ball reaches the ground in .64 seconds.

• Based on this information what is its acceleration?

The ball is free falling, which means that the acceleration is based on gravity. The acceleration due to gravity is an accepted value of 9.81 m/sec^2,

When I calculated this problem, my final answer was about 9.76 m/sec^2,which is close enough to the accepted value.

First I found the final velocity by using the equation

‘ds = vAve * ‘dt

2m = vAve * .64

3.125 = vAve

Now I can find the final velocity.

vAve = (v0+vf)/2

vAve = vf/2 (v0 is 0)

vf = 3.125 / 2

vf = 6.25 m /sec

Now I use the following equation to find acceleration.

vf^2 = v0^2 + 2a’ds

(6.25)^2 = 2a * 2

39.06 = 4a

a = 9.76 m /sec^2

answer/question/discussion:

• Is this consistent with an observation which concludes that a ball dropped from a height of 5 meters reaches the ground in 1.05 seconds?

For this problem my acceleration value was not as close to 9.8m/sec^2. However, it was still relatively close at 9.06 m /sec.

I did this the same way I did the first problem.

answer/question/discussion:

• Are these observations consistent with the accepted value of the acceleration of gravity, which is 9.8 m / s^2?

My answers were relatively close to this accepted value.

answer/question/discussion:

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Your work looks very good. Let me know if you have any questions. &#