Momentum hw problem, steel ball dropped from h

[physics1311]

Homework Statement

A steel ball of mass m falls from a height h onto a scale calibrated in Newtons. The ball rebounds repeatedly to nearly the same height h. The scale is sluggish in its response to the intermittent collisions and displays an average force Favg, such that FavgT = FΔt, where FΔt is the impulse that the ball imparts to the scale during the brief time Δt of each collision, and T is the time between collisions.

Calculate this average force in terms of m, h, and physical constants.

Homework Equations

momentum principle, delta(p)=Fnet delta(t)
update position, delta(r)=v(initial)delta(t) + a/2*delta(t)
delta(r) = v(avg)delta(t)
v(f)^2 =v(i)^2 +2a(∆x)

The Attempt at a Solution

use second equation
h=g/2*T^2 then rearange to get T= sqrt(2h/g)
(I think there's initial velocity, but I need help computing it)
that can be plugged into the final equation for T

I'm sort of lost on how to convert the impulse into different units and need help on this also

 

[BruceW]

Right. I think the first thing to do is to calculate the velocity at which the ball 'rebounds' from the ground. As soon as the ball leaves the ground, it is acted on only by gravity, and reaches a height h. And you want to know the velocity it had when it left the ground.

You've probably done this problem before under the title "maximum height a ball reaches when thrown vertically"