To find the relative pressure inside the can ([tex]\( p \)[/tex]) given the exit velocity ([tex]\( v \)[/tex]) of 42 feet per second, we can use the given formula:
[tex]\[ v = 7 \sqrt{p} \][/tex]
### Step-by-Step Solution:
1. Substitute the given velocity into the formula:
[tex]\[ 42 = 7 \sqrt{p} \][/tex]
2. Isolate the square root of [tex]\( p \)[/tex]:
Divide both sides of the equation by 7:
[tex]\[ \frac{42}{7} = \sqrt{p} \][/tex]
[tex]\[ 6 = \sqrt{p} \][/tex]
3. Eliminate the square root by squaring both sides:
[tex]\[ (6)^2 = (\sqrt{p})^2 \][/tex]
[tex]\[ 36 = p \][/tex]
The calculated relative pressure [tex]\( p \)[/tex] is 36 psi.
### Verification:
To ensure we have interpreted the results correctly, we round [tex]\( p \)[/tex] to the nearest integer if necessary. Here, [tex]\( p \)[/tex] is already an integer (36).
### Conclusion:
Thus, the relative pressure inside the can is:
[tex]\[ \boxed{36} \][/tex]
Correct Option:
C. 36 psi
