Free fall question

Question

1. A ball is thrown upward with initial velocity of 12m/s. How high will it go in 2.0s? What maximum height can it reach? What time does it need to reach the maximum height?

Answer 1

Assuming up is positive,

 

h(t) = -(1/2)gt² + v₀t + h₀

 

g = 9.8 m/s²

v₀ = 12 m/s

t = 2.0 s

h₀ = 0

 

Plug in the numbers and get 

 

h(2.0) = ? m

 

h_max is reached at the vertex of the height vs. time parabola, which occurs at

 

t = -v₀/[2(-g/2)] = v₀/g

 

Plug in the numbers.  Evaluate h at this value of t to get h_max.