Two skaters, Jo and Amba, are separately skating across a smooth, horizontal surface of ice - AQA - A-Level Maths Mechanics - Question 19 - 2021 - Paper 2

To find the shortest distance between the two parallel lines of motion, we first compute Jo's speed: $|Jo's \, speed| = \sqrt{(2.8)^2 + (9.6)^2} = \sqrt{7.84 + 92.16} = \sqrt{100} = 10 \, ms^{-1}.$ Now, we calculate the distance traveled by Jo in $4$ seconds: $Jo's \, distance = 10 \times 4 = 40 \, m.$ Next, we determine the distance traveled after 4 seconds by Amba: $Amba's \, distance = 8 \times 4 = 32 \, m.$ Finally, to find the shortest distance between the two lines when both positions are $5$ metres apart we calculate: $\text{Distance} = \sqrt{32^2 + 5^2} = \sqrt{1024 + 25} = \sqrt{1049} \approx 32.4 \, metres.$