Judging by the sketch, H is the vertical distance and D is the horizontal distance between where the bullet is shot and where it gets lodged in the wall. Let v₀ = 374 m/s, h = 0.45 m, and d = 9.6 m.
At time t, the bullet has
• horizontal position
• vertical position
Let t₁ and t₂ be the times when the bullet reaches the window and the wall, respectively. We want to find H and D given that
Eliminate D and H to get a system of equations involving t₁ and t₂ :
The first of these equations says
and substituting into the second equation gives
Solve for t₁ :
Solve for t₂ :
Now solve for H and D :