Nan’s suitcase is on a bench. The suitcase has a mass of 14 kilograms. Nan accidentally knocks the suitcase off the bench, and the suitcase falls at a speed of 2.7 meters per second. How much kinetic energy does the suitcase have just before it hits the floor?

Question

KE=12mv2

(1 point)
Responses

51.03 J
51.03 J

102.06 J
102.06 J

204.12 J
204.12 J

18.9 J

Answer 1

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:

\[ \boxed{51.03 , \text{J}} \]