A bullet traveling at 200 m/s strikes a soft wood and penetrates 4.5 cm through it before coming to rest. Calculate the bullet's average retardation
V^2 = Vo^2 + 2a*d.
V = 0, Vo = 200 m/s, d = 0.045 m., a = ?.
-4.44*10^5m/s^2
-4.44m/s2
To calculate the bullet's average retardation, you need to use the equation for average acceleration:
average acceleration = (final velocity - initial velocity) / time
In this case, the bullet comes to rest, so the final velocity is 0 m/s. The initial velocity is given as 200 m/s. We need to find the time it takes for the bullet to come to rest.
To find the time, we can use the equation of motion:
s = ut + (1/2)at^2
Where:
s = displacement (4.5 cm = 0.045 m)
u = initial velocity (200 m/s)
a = acceleration (which is the retardation in this case)
t = time
Rearranging the equation, we get:
t = √(2s / a)
Plugging in the values, we get:
t = √(2 * 0.045 / a)
Now, we can substitute the value of time into the equation for average acceleration:
average acceleration = (0 - 200) / (√(2 * 0.045 / a))
Simplifying, we have:
average acceleration = -200 / (√(2 * 0.045 / a))
Therefore, the bullet's average retardation can be calculated using the equation above.