To find the kinetic energy (KE) of the suitcase just before it hits the floor, we can use the formula:
\[ KE = \frac{1}{2} mv^2 \]
Where:
- \( m \) is the mass of the suitcase (14 kg),
- \( v \) is the velocity of the suitcase (2.7 m/s).
Substituting the values into the formula:
\[ KE = \frac{1}{2} \cdot 14 , \text{kg} \cdot (2.7 , \text{m/s})^2 \]
Calculating \( (2.7)^2 \):
\[ (2.7)^2 = 7.29 , \text{m}^2/\text{s}^2 \]
Then substituting back into the equation:
\[ KE = \frac{1}{2} \cdot 14 \cdot 7.29 \]
Calculating \( \frac{1}{2} \cdot 14 = 7 \):
\[ KE = 7 \cdot 7.29 = 51.03 , \text{J} \]
So, the kinetic energy of the suitcase just before it hits the floor is:
\[ \boxed{51.03 , \text{J}} \]