Question

There are two tall slides at the newly opened theme park, a blue slide and a red slide. The slides have such a height that, if it weren't for friction and air resistance, riders would travel twice as fast at the bottom of the blue slide as they do at the bottom of the red slide. If the red slide is 8m tall, how tall is the blue slide?

Answer 1

32 m

Step-by-step explanation:

By energy conservation, total energy at the top of slide must be equal to the total energy at at the bottom.

therefore

mgh = (1/2)mv^2

v^2= 2gh

`v = \sqrt(2gh)` ..............(1) i.e., velocity is a function of height of slide.

1st part

Let height of blue slide be H and height of red slide be h.

Let velocity of rider in blue slide= V and red slide= v

At the bottom of slide,

From equation (1)

therefore

`(V^(2))/(v^(2)) = (2gH)/(2gh)`

Given, V= 2v

`\therefore  \frac{4v^(2)}{v^2{}} = (H)/(h)`

H = 4h

therefore, height of blue slide is 4 times that of red slide= 4*8=32 m