Two identical twins, Amy and Beatrice, are on top of two different slides, one on each slide. Both slides start 3 m above the ground and end 0.5 m above the ground. Amy's slide is a straight, 45 degree slide with height given by h=−x+3 (so it starts at x=0 with a height of three meters and ends at x=2.5 with a height of half a meter). Beatrice's slide is curved and the height is given by h=3/(1+x) (so it starts at x=0 and ends at x=5). Both slides are frictionless.

Question

Two identical twins, Amy and Beatrice, are on top of two different slides, one on each slide. Both slides start 3 m above the ground and end 0.5 m above the ground. Amy's slide is a straight, 45 degree slide with height given by h=−x+3 (so it starts at x=0 with a height of three meters and ends at x=2.5 with a height of half a meter). Beatrice's slide is curved and the height is given by h=3/(1+x) (so it starts at x=0 and ends at x=5). Both slides are frictionless.
If both twins start from rest at the top of their slides, what is the ratio of Amy's speed to Beatrice's speed at the bottom of the slides? i.e., what is vAmy/vBeatrice?