To find the power of the gun, we will follow these steps:
### Step 1: Determine the kinetic energy of one bullet
The kinetic energy (KE) of one bullet can be calculated using the formula:
\[
KE = \frac{1}{2} mv^2
\]
where \( m \) is the mass of the bullet and \( v \) is its velocity.
### Step 2: Convert the mass of the bullet to kilograms
The mass of each bullet is given as 20 grams. We need to convert this to kilograms:
\[
m = 20 \, \text{g} = 20 \times 10^{-3} \, \text{kg} = 0.02 \, \text{kg}
\]
### Step 3: Convert the speed of the bullet to meters per second
The speed of the bullet is given as 360 km/h. We convert this to meters per second using the conversion factor \( \frac{5}{18} \):
\[
v = 360 \, \text{km/h} \times \frac{5}{18} = 100 \, \text{m/s}
\]
### Step 4: Calculate the kinetic energy of one bullet
Now, we can substitute the values of \( m \) and \( v \) into the kinetic energy formula:
\[
KE = \frac{1}{2} \times 0.02 \, \text{kg} \times (100 \, \text{m/s})^2
\]
\[
KE = \frac{1}{2} \times 0.02 \times 10000 = 100 \, \text{J}
\]
### Step 5: Calculate the total kinetic energy for all bullets fired in one minute
The gun fires 360 bullets per minute. Therefore, the total kinetic energy (TKE) for 360 bullets is:
\[
TKE = 360 \times KE = 360 \times 100 \, \text{J} = 36000 \, \text{J}
\]
### Step 6: Calculate the power of the gun
Power is defined as the total energy transferred per unit time. Since the bullets are fired in one minute (60 seconds), we can calculate the power (P) as follows:
\[
P = \frac{TKE}{\text{time}} = \frac{36000 \, \text{J}}{60 \, \text{s}} = 600 \, \text{W}
\]
### Final Answer
Thus, the power of the gun is:
\[
\text{Power} = 600 \, \text{W}
\]
