We have a bullet that penetrates through 20 identical wooden boards stacked together. The bullet starts with initial velocity v0 and comes to rest after passing through the 20th board. The key assumption is that the bullet experiences the same constant deceleration in each wooden board.
Now let's analyze the physics. Since the bullet experiences constant deceleration in each board, we can use kinematics equations. The velocity decreases according to the square root relationship shown in the graph. After passing through n boards, the velocity squared is proportional to the remaining distance.
To find the time relationship, we need to consider that each board has the same thickness. The time to pass through each board depends on the average velocity in that board. Since velocity decreases as the bullet progresses, later boards take longer to penetrate.
Now let's solve for the specific case of the 15th board. We calculate the velocities before and after the 15th board, find the average velocity, and determine the time ratio. After working through the mathematics, we find that the time to pass through the 15th board is approximately 0.313 times the total time t.