2022 EJC J1 MYE Q10

In a particular video animation, an animal \(X\) chases other animals. All animals only move in leaps in a straight line. You may assume that the time taken for each leap is the same and that the time in between leaps is negligible.

Animal \(X\) starts is chase by taking the first leap with a distance of \(\mathrm{5}\)m and each of its subsequent leaps is \(\mathrm{0}\mathrm{.02}\)m less than the previous.

1. Find the distance covered in the \(\mathrm{20}\)th leap and find the total distance covered in the first \(\mathrm{20}\) leaps by animal \(X\).[3]

Animal \(Y\) escapes from animal \(X\) by taking its first leap with a distance of \(\mathrm{5}\)m and each of its subsequent leaps is \(2\% \) shorter than the previous.

2. Given that animal \(Y\) is \(20\)m away from animal \(X\) at the start of the chase, find the least number of leaps for animal \(X\) to overtake animal \(Y\).[4]

Another animal \(Z\) escapes from animal \(X\) by taking leaps of constant distance \(\mathrm{4}\)m.

3. Given that animal \(Z\) is \(\mathrm{30}\)m away from animal \(X\) at the start of the chase, show that animal \(X\) will never catch animal \(Z\).[3]