You shake a bottle of soda and take off the cap. If the soda shoots out of the bottle with a velocity of 12 m/s, how high will it go?

Question

this is a physics question I can not understand it 

Answer 1

Solve this as a projectile problem with vertical motion at constant acceleration.

 

h(t) = -gt²/2 + v₀t + h₀

 

g = 9.8 m/s²

v₀ = 12 m/s

h₀ = 0

 

h(t) = -4.9t² + 12t

 

v(t) = -gt + v₀ = -9.8t + 12

 

Maximum height occurs when v(t) is instantaneously zero.

 

0 = -9.8t + 12

 

t = 12/9.8 s ≅ 1.224 s

 

Evaluate h(t) at t = 1.224 s to get h_max.  You can finish from here.