I will be making the assumption that you aren't actually really throwing the object over a bridge but rather dropping it as no initial velocity is actually given, which is required to do this problem. This will mean that initial velocity will be zero in this case.
First off, let's state all of the information we are given (the five kinematic quantities)
v₁ = 0 m/s
v₂ = cannot be determined
Δd = ?
Δt = 8 seconds
a (g) = 10 m/s² [down]
Now analyzing what we have, we can determine that we have 3 given quantities, 1 we must solve for, and 1 that cannot be found given our current information.
The five kinematic equations are useful because they all contain four kinematic quantities, and with different combinations too. In this case, we have three (v₁, Δt, a) and have to solve for Δd. The kinematic equation that fits with this would be:
Δd = v₁Δt + 0.5(a)(t)²
We can plug in our given values now.
Δd = 0 m/s(8 s) + 0.5(10 m/s²)(8 s)²
Δd = 0.5(10 m/s²)(8 s)²
Δd = 320 m
Therefore, the total displacement of the object would have to be 300m. (Due to significant digit rules)
