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, substituting the values into the formula:
\[ KE = \frac{1}{2} \times 14 , \text{kg} \times (2.7 , \text{m/s})^2 \]
First, calculate \( (2.7)^2 \):
\[ (2.7)^2 = 7.29 \]
Now plug it back into the equation:
\[ KE = \frac{1}{2} \times 14 , \text{kg} \times 7.29 , \text{m}^2/\text{s}^2 \]
Calculating:
\[ KE = 7 \times 7.29 = 51.03 , \text{J} \]
Therefore, the kinetic energy of the suitcase just before it hits the floor is:
51.03 J