Consider again the brachistochrone problem but suppose that

Consider again the brachistochrone problem but suppose that the car is launched from point 1 with a ?xed speed v0.

Solution

From kinematic equations, distance travelled by the object is

       s = v² - u² / 2 g

Here, v is final speed , u is initial speed.

At maximum height speed of the object is zero. so v =0

since the object is moving away from the earth, g = - g

s = -v₀² / 2 ( - g )

   = v₀² / 2g