Sure, let's work through the problem step by step.
We are tasked with finding the kinetic energy of a bullet with a mass of 0.162 kg, traveling at a velocity of 800 m/s as it leaves the muzzle of a gun.
### Step-by-Step Solution:
1. Understand the problem:
- We need to find the kinetic energy of the bullet.
- The mass of the bullet, [tex]\( m \)[/tex], is 0.162 kg.
- The velocity of the bullet, [tex]\( v \)[/tex], is 800 m/s.
2. Know the formula:
- The formula for kinetic energy [tex]\( (KE) \)[/tex] is given by:
[tex]\[
KE = \frac{1}{2} m v^2
\][/tex]
- Here, [tex]\( m \)[/tex] is the mass of the object, and [tex]\( v \)[/tex] is its velocity.
3. Plug in the values:
- Substitute [tex]\( m = 0.162 \, \text{kg} \)[/tex] and [tex]\( v = 800 \, \text{m/s} \)[/tex] into the kinetic energy formula:
[tex]\[
KE = \frac{1}{2} \cdot 0.162 \, \text{kg} \cdot (800 \, \text{m/s})^2
\][/tex]
4. Calculate the velocity squared:
- First, calculate [tex]\( (800 \, \text{m/s})^2 \)[/tex]:
[tex]\[
(800 \, \text{m/s})^2 = 640000 \, \text{m}^2/\text{s}^2
\][/tex]
5. Calculate the product:
- Multiply [tex]\( 0.162 \)[/tex] by [tex]\( 640000 \)[/tex]:
[tex]\[
0.162 \times 640000 = 103680 \, \text{kg} \cdot \text{m}^2/\text{s}^2
\][/tex]
6. Divide by 2:
- Finally, divide by 2 to get the kinetic energy:
[tex]\[
KE = \frac{103680}{2} = 51840 \, \text{J}
\][/tex]
### Conclusion:
The kinetic energy of the bullet as it leaves the muzzle of the gun is [tex]\( 51840 \, \text{J} \)[/tex].
