A ball is thrown vertically upwards from the ground. It rises to a height of 15 m

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A ball is thrown vertically upwards from the ground. It rises to a height of 15 m and then falls and bounces. After each bounce it rises vertically to 5/8 of the height from which it fell.

a. Find the height to which the ball bounces after the nth impact with the ground.

b. Find the total distance travelled by the ball from the first throw to the tenth impact with the ground.

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