Question

Wes and Lindsay stand on the roof of a building. Wes leans over the edge and drops an apple. Lindsay waits, 1.25s afrer Wes releases his fruit and throws an orange straight down at 28 m/s. Both pieces of fruit hit the ground simultaneously. Calculate the common height from which the fruit were released. Ignore the effects of air resistence.

Answer 1

Start counting time when the apple is thrown. The distance it falls is
D1 = (g/2)t^2 = 4.9 t^2
For the orange, for t>1.25 s,
D2 = 28(t-1.25) + 4.9(t-1.25)^2
Set D1 = D2 and solve for t when they are both at the same distance (ground level).

4.9t^2 = 28(t-1.25) + 4.9(t-1.25)^2
= 28(t-1.25) + 4.9t^2 -12.25 t + 7.656

0 = 15.75 t - 27.34
t = 1.736 s
Use that t in the D1 formula for the building height.
I get 14.8 meters. Check my math.