You drop a water balloon off of a tree branch, and you time the drop time at Δt = 0.8 sec, from the instant you drop it to the instant it impacts the sidewalk.

h = 0.5g*t^2 = 4.9*0.8^2 =

To find the height of the tree branch, we can use the equation of motion in the vertical direction (assuming no air resistance):

h = (1/2) * g * Δt^2

Where:
h = height of the tree branch
g = acceleration due to gravity (approximately 9.8 m/s^2)
Δt = time taken for the water balloon to drop (0.8 sec)

Substituting the known values into the equation:

h = (1/2) * 9.8 * (0.8)^2
h = 3.136 meters

Therefore, the height of the tree branch is approximately 3.136 meters.