Nan’s suitcase is on a bench. The suitcase has a mass of 14

Nan’s suitcase is on a bench. The suitcase has a mass of 14 kilograms. Nan accidentally knocks the suitcase off the bench, and the suitcase falls at a speed of 2.7 meters per second. How much kinetic energy does the suitcase have just before it hits the floor? KE=12mv2 (1 point) Responses 51.03 J 51.03 J 204.12 J 204.12 J 18.9 J 18.9 J 102.06 J

1 answer

To calculate the kinetic energy (KE) of the suitcase just before it hits the floor, we can use the formula:

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

where:

\( m \) is the mass of the suitcase (in kilograms)
\( v \) is the velocity (in meters per second)

Given:

\( m = 14 \) kg
\( v = 2.7 \) m/s

Substituting the values into the formula:

\[ KE = \frac{1}{2} \times 14 , \text{kg} \times (2.7 , \text{m/s})^2 \] \[ KE = \frac{1}{2} \times 14 \times 7.29 , \text{m}^2/\text{s}^2 \quad \text{(since } 2.7^2 = 7.29\text{)} \] \[ KE = 7 \times 7.29 \] \[ KE = 51.03 , \text{J} \]

So, the kinetic energy of the suitcase just before it hits the floor is 51.03 J.