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?
KE = 1/2mv^2
a. 204.12 J
b. 18.9 J
c. 102.06 J
d. 51.03 J
To calculate the kinetic energy (KE) of the suitcase just before it hits the floor, we can use the formula KE = 1/2mv^2, where m is the mass of the suitcase and v is its speed.
Given:
m = 14 kilograms
v = 2.7 meters per second
Plugging these values into the formula, we get:
KE = 1/2 * 14 kg * (2.7 m/s)^2
Simplifying the expression inside the parentheses first:
(2.7 m/s)^2 = 2.7^2 m^2/s^2 = 7.29 m^2/s^2
Now, substituting this value back into the equation:
KE = 1/2 * 14 kg * 7.29 m^2/s^2
Simplifying further:
KE = 7 * 7.29 kg⋅m^2/s^2
KE = 50.97 kg⋅m^2/s^2
KE ≈ 51.03 J
Therefore, the kinetic energy of the suitcase just before it hits the floor is approximately 51.03 J.
The correct answer is d. 51.03 J.