A ball is dropped from a height of 12 m and it rebounds ½ of the distance it falls. If it continues to fall and rebound in this way, how far will it travel before coming to rest?

36 m

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30 m

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48 m

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60 m

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Solution

The total distance travelled by the ball:
12 + 2(6 + 3 + 1.5 + …) For a decreasing geometric progression, the sum to infinite number of terms is:
S∞ = a1-r, a= first term, r<1
So, the total distance travelled by the ball:
= 12 + 2(6 + 3 + 1.5 + …)
=12+261-0.5 = 36m

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A ball is dropped from a height of 12 m and it rebounds ½ of the distance it falls. If it continues to fall and rebound in this way, how far will it travel before coming to rest?

The total distance travelled by the ball:12 + 2(6 + 3 + 1.5 + …) For a decreasing geometric progression, the sum to infinite number of terms is:​ S∞ = a1-r, a= first term, r<1So, the total distance travelled by the ball:= 12 + 2(6 + 3 + 1.5 + …) =12+261-0.5 = 36m

The total distance travelled by the ball:
12 + 2(6 + 3 + 1.5 + …) For a decreasing geometric progression, the sum to infinite number of terms is:
S∞ = a1-r, a= first term, r<1
So, the total distance travelled by the ball:
= 12 + 2(6 + 3 + 1.5 + …)
=12+261-0.5 = 36m