A ball is tossed to a height of 4 meters rebounds to 40% of its previous height. Find the distance the ball has travelled when it strikes the ground for the fifth time.
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40% of its previous height until it stops.
Step-by-step explanation:
Toss up 4m
1st drop 4m
1st rebound 4(0.4)
2nd drop 4(0.4)
2nd rebound 4(0.4)^2
3rd drop 4(0.4)^2
3rd rebound 4(0.4)^3
4th drop 4(0.4)^3
4th rebound 4(0.4)^4
5th drop 4(0.4)^4
Including the original 4m toss
Total distance travelled = 4m + ∑ drops+ ∑rebounds
= 4 + ∑ 4+4(0.4)+4(0.4)^2+.. + 4(0.4)^4
+∑4(0.4)+4(0.4)^2 + …….+4(0.4)^4
= 2∑4+4(0.4)+4(0.4)^2 + …….+4(0.4)^4
= 2 a(1-r^n)/(1-r)
= 2(4)(1–0.4^5)/(1–0.4) = 8(0.98976)/0.6
= 13.197 m
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