To determine the mass of the bowling ball, we can use the formula for kinetic energy:
[tex]\[ KE = \frac{1}{2}mv^2 \][/tex]
Rearranging this formula to solve for mass [tex]\( m \)[/tex], we get:
[tex]\[ m = \frac{2KE}{v^2} \][/tex]
Given values:
- [tex]\( KE = 1.8 \)[/tex] joules
- [tex]\( v = 2 \)[/tex] meters per second
Plug these values into the formula:
[tex]\[ m = \frac{2 \times 1.8}{2^2} \][/tex]
First, calculate the square of the velocity:
[tex]\[ 2^2 = 4 \][/tex]
Next, multiply the kinetic energy by 2:
[tex]\[ 2 \times 1.8 = 3.6 \][/tex]
Now, divide by the square of the velocity:
[tex]\[ m = \frac{3.6}{4} = 0.9 \][/tex]
Thus, the mass of the bowling ball is [tex]\( \boxed{0.9} \)[/tex] kilograms.
