A bullet is fired through a wooden board with a thickness of 8.0 cm. The bullet hits the board perpendicular to it, and with a speed of +350 m/s. The bullet then emerges on the other side of the board with a speed of +210 m/s. Assuming constant acceleration (rather, deceleration!) of the bullet while inside the wooden board, calculate the acceleration.
To calculate the acceleration of the bullet while inside the wooden board, we can use the following equation:
v^2 = u^2 + 2as
Where:
- v is the final velocity of the bullet (210 m/s),
- u is the initial velocity of the bullet (350 m/s),
- a is the acceleration of the bullet, and
- s is the distance traveled by the bullet inside the board (8.0 cm or 0.08 m).
Before proceeding further, we need to convert the thickness of the wooden board to meters. Thus, 8.0 cm is equal to 0.08 m.
Now, let's rearrange the equation to solve for acceleration:
a = (v^2 - u^2) / (2s)
Plugging in the given values, we have:
a = (210^2 - 350^2) / (2 * 0.08)
Now, let's calculate the value.
a = (44100 - 122500) / 0.16
a = -78400 / 0.16
a = -490000 m/s^2
Therefore, the acceleration of the bullet while inside the wooden board is -490,000 m/s^2. The negative sign indicates that the bullet is decelerating.