Given the acceleration, initial velocity, and initial position of a ball thrown vertically upward, how long does it take for it to reach its maximum height? what is the maximum height?

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

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the answer is false. this is because for ice to melt, it requires latent heat of melting. latent heat means heat energy required to change phase without any increase in temperatures. therefore, the ice will take energy from the environment to melt hence atmospheric temperatures will reduce.