Height of the building = x
height of third bounce = 6.75 m
Number of bounce = 3
Equation (Geometric sequence formula):
(3/4)³ (x) = 6.75
(27/64) (x) = 6.75
(64/27) [ (27/64)(x) = 6.75 ] (64/27)
x = (6.75) (64/27)
x = 432/27
x = 16
ANSWER: The height (of the building) from which the ball was dropped
is 16 m.
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Check:
To find the height of second bounce:
6.75 = height of the 3rd bounce.
x₂ = height of the second bounce
Since 6.75 is 3/4 of the height of the previous bounce x₂, then:
3/4 (x₂) = 6.75
(4/3) [3/4 (x₂) = 6.75 ] (4/3)
x₂ = 6.75 (4/3)
x₂ = 9 m, height of the second bounce
To find the height of first bounce:
9 m = height of the second bounce
x₁ = height of the first bounce
Since 9 m is 3/4 of the first bounce x₁, then:
3/4 (x₁) = 9
(4/3) [ 3/4 (x₁) = 9] (4/3)
x₁ = 12 , height of the first bounce
To find the height from where the ball was dropped:
12 m = height of the first bounce
x = height of the building
Since 12 m is 3/4 of the height from where the ball was dropped, then:
3/4 (x) = 12
(4/3) [ 3/4(x) = 12)] (4/3)
x = 12 (4/3)
x = 16 m, the height from where the object was dropped.
