Interactive practice questions
A ball dropped from a height of $24$24 metres will bounce back off the ground to $60%$60% of the height of the previous bounce (or the height from which it is dropped when considering the first bounce).
Write a function, $y$y, to represent the height of the $n$nth bounce.
Find the height of the fifth bounce. Give your answer correct to two decimal places.
When a ball is dropped onto a horizontal surface from a height of $6$6 metres, it reaches a vertical height of $50%$50% of the starting height on its first bounce. It continues to reach a height of $50%$50% of the previous height in each subsequent bounce.
When a marble is rolled horizontally on a flat surface it rolls $30$30 cm in the first second. It then rolls $60%$60% of the distance travelled in the previous second, for each subsequent second.
Consider the series $8+1+\frac{1}{8}$8+1+18$\dots$…
Find the sum of the first $7$7 terms. Round your answer to three decimal places if necessary.