Two balls are thrown upward from the edge of the cliff.
The first is thrown with a speed of 48ft/s and the other is thrown a
second later with a speed of 24 ft/s.
Do the balls ever pass each other?
Yes.
Let the origin be the point where the balls are thrown upward and set a +y direction upward.
The first ball has the position equation:
y = y0 + v0*t + (1/2)at^2
y = 48t - 16t^2
The second ball has a position equation:
y = y0 + v0*(t - 1) + (1/2)a(t - 1)^2 <-- Since it is launched 1 s later.
y = 24(t - 1) - 16(t - 1)^2
y = -16t^2 + 56t - 40
When do these two y values equal each other? When
48t - 16t^2 = -16t^2 + 56t - 40
-8t = -40
t =5 s
-Dan