Answer:
ymax= y₀ + v₀²/2g
Explanation:
The equations of uniformly accelerated rectilinear motion of upward (vertical) for the y axis are :
vfy = v₀y-gt Formula (1)
vfy² = v₀y²-2gΔy Formula (2)
Where:
t: time in any position (s)
Δy= y-y₀
y = vertical position in any time (m)
y₀ : initial vertical position in meters (m)
v₀y: initial vertical velocity in m/s
vfy: final vertical velocity in m/s
g: acceleration due to gravity in m/s²
Data
v₀y = v₀ : total initial speed of the ball
y₀ : initial vertical position of the ball
g :acceleration due to gravity
Time (t) calculation for the ball to reach maximum height
We apply the formula (1)
vfy = v₀y-gt
When the ball reaches its maximum height (h), vy = 0:
0= v₀-gt
v₀ = gt
Calculation of the maximum hight that reaches the ball
When the ball reaches its maximum height (ymax), vy = 0:
We apply the formula (2)
vfy²= v₀y²-2gΔy
0= v₀²-2gΔy
2gΔy = v₀²
Δy= v₀²/2g ,Δy= ymax-y₀
ymax-y₀ = v₀²/2g
ymax= y₀ + v₀²/2g