To calculate the average velocity of the bullet as it penetrates the tree, we need to use the concept of average velocity in uniform motion. Here is a step-by-step solution:
1. Identify the initial velocity (u):
The initial velocity of the bullet is given as [tex]\( u = 100 \, \text{m/s} \)[/tex].
2. Identify the final velocity (v):
The final velocity of the bullet, after it comes to rest inside the tree, is [tex]\( v = 0 \, \text{m/s} \)[/tex] since the bullet comes to a stop.
3. Calculate the average velocity (v_avg):
The formula for average velocity when considering uniform acceleration is given by:
[tex]\[
v_{\text{avg}} = \frac{u + v}{2}
\][/tex]
Plugging in the values:
[tex]\[
v_{\text{avg}} = \frac{100 + 0}{2}
\][/tex]
4. Perform the calculation:
[tex]\[
v_{\text{avg}} = \frac{100}{2} = 50 \, \text{m/s}
\][/tex]
Therefore, the average velocity of the bullet as it penetrates the tree is [tex]\( 50 \, \text{m/s} \)[/tex].
