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 (14 kg)
- \( v \) is the velocity (2.7 m/s)
Plugging in the values:
\[ KE = \frac{1}{2} \times 14 , \text{kg} \times (2.7 , \text{m/s})^2 \]
First, calculate \( (2.7 , \text{m/s})^2 \):
\[ (2.7)^2 = 7.29 , \text{m}^2/\text{s}^2 \]
Now substitute this value back into the KE formula:
\[ KE = \frac{1}{2} \times 14 \times 7.29 \]
Calculating this gives:
\[ KE = 7 \times 7.29 = 51.03 , \text{J} \]
So the kinetic energy of the suitcase just before it hits the floor is 51.03 J.