Suppose you drop a ball from a window 40 meter above the ground.The ball bounces 70% of the previous height each bounce.What is the total number of meters the ball travels between the time it dropped and the tenth bounce?
+26400 Suppose you drop a ball from a window 40 meter above the ground.The ball bounces 70% of the previous height each bounce.What is the total number of meters the ball travels between the time it dropped and the tenth bounce?
geometric sequence
\(a_1 = 40\ m \\ r = 70\ \% = 0.7\)
\(\begin{array}{rcll} s &=& a_1 \left( \frac{1-r^{11}}{1-r} \right) \\ s &=& 40 \left( \frac{1-0.7^{11}}{1-0.7} \right) \\ s &=& 40 \left( \frac{1-0.01977326743}{1-0.7} \right) \\ s &=& 40 \left( \frac{0.98022673257}{0.3} \right) \\ s &=& 40 \cdot 3.26742244190 \\ s &=& 130.696897676\ m \end{array}\)
+26400 1. Ball up: n=11
\(\small{\begin{array}{lrcll} 1. \text{ Ball up }: \qquad && s_{10} = 40\cdot ( \frac{1-0.7^{10}}{1-0.7} ) &=& 129.5669967\ m\\ 2.\text{ Ball down }: \qquad &+& s_{10} = 40 \cdot ( \frac{1-0.7^{10}}{1-0.7} ) &=& 129.5669967\ m\\ 3.\text{}: \qquad &-& &&40\ m \\ \end{array}}\)
= 2 * 129.5669967 - 40 m
= 219.1339934 m
