Questions: A ball has a kinetic energy of 4.50 kJ . If the ball has a mass of 120.0 g , how fast is the ball traveling, in meters per second?

Solution Steps

First, we need to convert the mass of the ball from grams to kilograms because the standard unit of mass in the kinetic energy formula is kilograms.

\[ 120.0 \, \text{g} = 0.1200 \, \text{kg} \]

The kinetic energy (KE) of an object is given by the formula:

\[ KE = \frac{1}{2} m v^2 \]

where \( KE \) is the kinetic energy, \( m \) is the mass, and \( v \) is the velocity. We need to solve for \( v \).

Rearrange the formula to solve for \( v \):

\[ v = \sqrt{\frac{2 \cdot KE}{m}} \]

Substitute the given values into the formula:

\[ v = \sqrt{\frac{2 \cdot 4500 \, \text{J}}{0.1200 \, \text{kg}}} \]

Perform the calculation:

\[ v = \sqrt{\frac{9000 \, \text{J}}{0.1200 \, \text{kg}}} = \sqrt{75000 \, \text{m}^2/\text{s}^2} = 273.9 \, \text{m/s} \]

Final Answer