To calculate the kinetic energy (KE) of the suitcase just before it hits the floor, you can use the formula:
\[ KE = \frac{1}{2} mv^2 \]
where:
- \( m \) is the mass of the suitcase (14 kg),
- \( v \) is the velocity (2.7 m/s).
Now, substituting the values into the formula:
\[ KE = \frac{1}{2} \times 14 , \text{kg} \times (2.7 , \text{m/s})^2 \]
First, calculate the speed squared:
\[ (2.7 , \text{m/s})^2 = 7.29 , \text{m}^2/\text{s}^2 \]
Now substituting that back in:
\[ KE = \frac{1}{2} \times 14 , \text{kg} \times 7.29 , \text{m}^2/\text{s}^2 \]
\[ KE = 7 \times 7.29 = 51.03 , \text{J} \]
Therefore, the kinetic energy of the suitcase just before it hits the floor is 51.03 J.