Question

A certain ball is dropped from a height of 𝑥 feet. It always bounces up to $\frac{2}{3}x$ feet. Suppose the ball is dropped from 10 feet and is stopped exactly when it touches the ground after the 3rd bounce. What is the total distance traveled by the ball? Express your answer in exponential notation.

• A. $10+2[10\times (2/3)+10\times (2/3{)}^2+10\times \left(2/3{)}^3\right]$
• B. $2[10+10\times (2/3)+10\times (2/3{)}^2+10\times \left(2/3{)}^3\right]$
• C. $2[10\times (2/3)+10\times (2/3{)}^2+10\times \left(2/3{)}^3\right]$
• D. $10+10\times \left(2/3\right)+10\times (2/3{)}^2+10\times (2/3{)}^3$

Answer 1

The correct option is A $10+2[10\times (2/3)+10\times (2/3{)}^2+10\times \left(2/3{)}^3\right]$

Total distance travelled = $10+2[10\times (2/3)+10\times (2/3{)}^2+10\times \left(2/3{)}^3\right]$