Ayub drops a ball from a height of 6.25 metres to the flat ground below. After the third bounce, the ball rises to a height of 40 cm read more...

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Q.

Ayub drops a ball from a height of 6.25 metres to the flat ground below. After the third bounce, the ball rises to a height of 40 cm. The height to which the ball rises after each bounce is the same fraction of the height reached on its previous bounce. What is the fraction?

 #  Solution :

Let the height of bounce be h0, h1, h2 and h3 and the fraction be a.

Here,
h0 = 6.25m = 625cm (Given)
h3 = 40 cm (Given)

Now, Each succeeding height is the fraction of previous height...

Therefore,
h1 = h0 x a ----(Equation 1)
h2 = h1 x a ----(Equation 2)
h3 = h2 x a ----(Equation 3)

Now,
Substitute the value of h1 in Eq. 2 with Eq. 1
h2 = (h0 x a) x a
∴ h2 = h0 x a² ----(Equation 4)

Similarly,
Substitute the value of h2 in Eq. 3 with Eq. 4
h3 = (h0 x a²) x a
∴ h3 = h0 x a³----(Equation 5)

Now, Put h3 = 40(Given) and h0 = 625(Given) in Equation 5
40 = 625 x a³
40/625 = a³
(40 ÷ 5 / 625 ÷ 5) = a³
8/125 = a^3
3√(8/125) = a
2/5 = a
∴ Fraction = 2/5

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Lets check & verify the answer

Put a = 2/5 in Equation 1, 2 and 3

h1 = h0 x a ----(Equation 1)
h1 = 625 x 2/5
h1 = 250 cm

h2 = h1 x a ----(Equation 2)
h2 = 250 x 2/5
h2 = 100 cm

h3 = h2 x a ----(Equation 3)
h3 = 100 x 2/5
h3 = 40 cm