You drop a ball from a stair case that is 36 ft high. By the time you get down the stairs to measure the height of the bounce, the ball has bounced four times and has a height of 2.25 ft after its fourth bounce. How high did the ball bounce after it first hit the floor?

The height should be 18 feet.

Given that,

Based on the above information, the calculation is as follows:

The first height is 36 feet.

Now after the first bounce, it will be 36r

Here r is the ratio of the height

In the second bounce, the height is

In the third bounce, the height is

In the fourth bounce, the height is , and this value is 2.25 ft, so:

Now

r = 0.5

Now  

So, after the first bounce, the height is:

= 36r

= 36(0.5)

= 18 feet

Therefore we can conclude that The height should be 18 feet.

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18 feet

Step-by-step explanation:

After each bounce, the ball reaches only a percentage of the maximum height it reached before.

The first height is 36 feet, after the first bounce, it will be 36*r, where r is the ratio of the height the ball can still reach by the previous maximum height.

In the second bounce, the height is 36*r^2

In the third bounce, the height is 36*r^3

In the fourth bounce, the height is 36*r^4, and this value is 2.25 ft, so:

36*r^4 = 2.25

r^4 = 2.25/36

r^4 =  0.0625

r = 0.5

So, after the first bounce, the height is:

36*r = 36*0.5 = 18 feet