V^2 = Vo^2 + 2a*d
V = 333 m/s.
Vo = 370 m/s.
d = 12 cm = 0.12 m.
Solve for a. It will be negative.
V = 333 m/s.
Vo = 370 m/s.
d = 12 cm = 0.12 m.
Solve for a. It will be negative.
v^2 = u^2 + 2as
Where:
- v = final velocity of the bullet (333 m/s)
- u = initial velocity of the bullet (370 m/s)
- a = acceleration of the bullet while inside the board (unknown)
- s = displacement of the bullet (thickness of the board = 12.0 cm = 0.12 m)
Rearranging the equation, we get:
a = (v^2 - u^2) / (2s)
Substituting the given values, we have:
a = (333^2 - 370^2) / (2 * 0.12)
Simplifying the equation, we get:
a = (-47239) / (0.24)
a ≈ -196,829 m/s^2
Therefore, the acceleration of the bullet while inside the wooden board is approximately -196,829 m/s^2
v^2 = u^2 + 2as
where:
v = final velocity of the bullet (+333 m/s)
u = initial velocity of the bullet (+370 m/s)
a = acceleration of the bullet (we need to find this)
s = distance traveled by the bullet inside the board (twice the thickness of the board)
First, let's determine the distance traveled by the bullet inside the board. It is given that the thickness of the board is 12.0 cm or 0.12 m. Since the bullet enters and exits the board fully, the distance traveled inside the board is twice the thickness, which is 2 * 0.12 m = 0.24 m.
Now, we can plug the given values into the equation of motion:
(333 m/s)^2 = (370 m/s)^2 + 2 * a * 0.24 m
Simplifying the equation:
(333 m/s)^2 - (370 m/s)^2 = 2 * a * 0.24 m
Using a calculator:
110889 m^2/s^2 - 136900 m^2/s^2 = 0.48 m * a
-26011 m^2/s^2 = 0.48 m * a
To find the acceleration, we rearrange the equation:
a = -26011 m^2/s^2 / 0.48 m
Calculating:
a ≈ -54148 m/s^2
So, the acceleration of the bullet while inside the wooden board is approximately -54148 m/s^2, which indicates that the bullet is experiencing deceleration.