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

  the unit of the measure =

explanation:

  the property that is quantified by the energy needed per of material to raise the temperature by one.

  si unit of energy = joule (j)

  si unit of temperature = kelvin (k)

  si unit of mass of material = kilogram (kg)

the property that is quantified by the energy needed per of material to raise the temperature by one is called specific heat.

the unit of specific heat is

the inner core.

good luck: )

klicker