Speed of objects as they hit the ground

[yrjosmiel]

Let's say there are two objects. One is thrown directly downward at v0 and the other is thrown horizontally (90 degrees) at v0, both from height h. Which object will have a higher speed by the time they hit the ground? Would they have the same speed?

For the object thrown downward...
h = (vf² - v0²)/2a
vf_{y axis} = sqrt(v0² + 2ah)
final speed = sqrt(v0² + 2ah)

For the object thrown horizontally
v_{y axis} = sqrt(2ah)
v_{x axis} = v0
add the two vectors
vf_total = sqrt(v0² + 2ah)

Is this right? Or have I miscalculated something in the way?

 

[A.T.]

You can also use energy conservation here.

 

[A Lazy Shisno]

Looks good to me. The matching velocities speeds make sense when you consider conservation of energy.

 

[CWatters]

The velocities won't be the same but the speeds will.