An object is launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. What is the value for s,

Question

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high.
What is the value for ,v, the initial speed?

 

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high.
At what time will the object reach its maximum height?

 

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high.
What is the object's maximum height?

 

all these questions are related, but each asks about a specific thing 

 

The two formulas that you need are:

h = -16t2 + s

h = -16t2 +vt + s

 

Answer 1

h(t) = at²/2 + v₀t + h₀

 

a = -g = -32 ft/s²

v₀ = initial vertical speed = 64 ft/s

h₀ = 80 ft

 

h(t) = -16t² + 64t + 80,

 

with t in seconds, h in feet.  Time to maximum height is at the vertex of the height-vs.-time parabola, which is at

 

t = -64/[2(-16)] sec = ? sec

 

Evaluate h(t) at this value of t to get the maximum height.