Sure! To find the mass of an object given its kinetic energy and velocity, we can use the formula for kinetic energy:
[tex]\[ KE = \frac{1}{2} mv^2 \][/tex]
Here, [tex]\( KE \)[/tex] stands for the kinetic energy, [tex]\( m \)[/tex] is the mass, and [tex]\( v \)[/tex] is the velocity.
Given:
- Kinetic Energy, [tex]\( KE = 480 \)[/tex] Joules
- Velocity, [tex]\( v = 8 \)[/tex] m/s
We need to solve for the mass [tex]\( m \)[/tex]. Let's rearrange the formula to isolate [tex]\( m \)[/tex]:
1. Start with the kinetic energy formula:
[tex]\[ KE = \frac{1}{2} mv^2 \][/tex]
2. Multiply both sides of the equation by 2 to get rid of the fraction:
[tex]\[ 2 \times KE = mv^2 \][/tex]
[tex]\[ 2 \times 480 = 8m^2 \][/tex]
[tex]\[ 960 = mv^2 \][/tex]
3. Divide both sides by [tex]\( v^2 \)[/tex] to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{2 \times KE}{v^2} \][/tex]
[tex]\[ m = \frac{960}{64} \][/tex]
After performing the division, we get:
[tex]\[ m = 15.0 \][/tex]
Therefore, the mass of the object is [tex]\( 15.0 \)[/tex] kilograms.
