I don't think u need an equation for this.
Let x be the time after the 2nd ball has passed
Assume that g=10ms^-1
10x + 10x = 2.4m
20x = 2.4m
x = 0.12 second
The heat source will have to heat up the air before you could feel the temperature, or get burned by it.
While when you simply touch the cake tin, heat directly transfers to yr finger, that's why you get burnt instantaneously