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 speed of the suitcase (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 \( (2.7 , \text{m/s})^2 \):
\[ (2.7)^2 = 7.29 , \text{m}^2/\text{s}^2 \]
Now, substitute back into the KE formula:
\[ KE = \frac{1}{2} \times 14 \times 7.29 \]
Calculating \( \frac{1}{2} \times 14 \):
\[ \frac{1}{2} \times 14 = 7 \]
Now, multiply that by 7.29:
\[ KE = 7 \times 7.29 = 51.03 , \text{J} \]
Thus, the kinetic energy of the suitcase just before it hits the floor is:
51.03 J