To calculate 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 in kilograms,
- \( v \) is the velocity in meters per second.
Given:
- \( m = 14 \) kg
- \( v = 2.7 \) m/s
Now, we can substitute the values into the formula:
\[ KE = \frac{1}{2} \times 14 , \text{kg} \times (2.7 , \text{m/s})^2 \]
Calculating \( (2.7)^2 \):
\[ (2.7)^2 = 7.29 \]
Now substituting back into the kinetic energy formula:
\[ KE = \frac{1}{2} \times 14 \times 7.29 \]
Calculating \(\frac{1}{2} \times 14\):
\[ \frac{1}{2} \times 14 = 7 \]
Now we can calculate the kinetic energy:
\[ KE = 7 \times 7.29 = 51.03 , \text{J} \]
Thus, the kinetic energy of the suitcase just before it hits the floor is:
\[ \text{51.03 J} \]
So the correct response is 51.03 J.