Let's solve this step-by-step.
We are given:
- The kinetic energy of the bowling ball, [tex]\( KE \)[/tex], which is 1.8 joules.
- The speed of the bowling ball, [tex]\( v \)[/tex], which is 2 meters/second.
We need to calculate the mass of the bowling ball using the formula:
[tex]\[ m = \frac{2 KE}{v^2} \][/tex]
Step 1: Plug in the values for kinetic energy and speed into the formula:
[tex]\[ m = \frac{2 \times 1.8}{2^2} \][/tex]
Step 2: Calculate the squared speed:
[tex]\[ 2^2 = 4 \][/tex]
Step 3: Substitute the squared speed into the equation:
[tex]\[ m = \frac{2 \times 1.8}{4} \][/tex]
Step 4: Multiply the kinetic energy by 2:
[tex]\[ 2 \times 1.8 = 3.6 \][/tex]
Step 5: Divide by the squared speed:
[tex]\[ m = \frac{3.6}{4} \][/tex]
Step 6: Calculate the result:
[tex]\[ m = 0.9 \][/tex]
So, the mass of the bowling ball is [tex]\( \boxed{0.9} \)[/tex] kilograms.
