Answer:
The velocity is  [tex]v_h = 19.2 \ m/s[/tex]
Explanation:
From the question we are told that
  The speed of the roller coaster at ground level  is [tex]v = 26 \ m/s[/tex]
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Generally we can define the roller coaster speed at ground level using the an equation of motion as
   [tex]v^2 = u^2 + 2 g s[/tex]
 u is  zero given that the roller coaster started from rest
   So
      [tex]26^2 = 0 + 2 * g * s[/tex]
So Â
      [tex]s = \frac{26^2}{ 2 * g }[/tex]
=> Â Â Â [tex]s = 37.6 \ m[/tex]
Now the displacement half way is mathematically represented as
   Â
  [tex]s_{h} = \frac{37.6}{2}[/tex]
   [tex]s_{h} = 18.8 \ m[/tex]
So
   [tex]v_h ^2 = u^2 + 2 * g * s_h[/tex]
Where  [tex]v_h[/tex] is the velocity at the half way point
=> Â [tex]v_h = \sqrt{ 0 + 2 * 9.8 * 18.8 }[/tex]
=> Â [tex]v_h = 19.2 \ m/s[/tex]
