Question

a (2.56\text{ kg}) box is thrown with (87.0\text{ j}) of kinetic energy.

what is the velocity of the box?

(v = ?\text{ m/s})

Explanation:

⚡ Using what you learned: kinetic energy and the work-energy theorem

Step 1: Identify given values

$$ m = 2.56\text{ kg} $$

$$ KE = 87.0\text{ J} $$

Step 2: Set up the kinetic energy formula

$$ KE = \frac{1}{2}mv^2 $$

Step 3: Solve for velocity \(v\)

$$ 87.0 = \frac{1}{2}(2.56)v^2 $$

$$ 87.0 = 1.28v^2 $$

$$ v^2 = \frac{87.0}{1.28} \approx 67.96875 $$

$$ v = \sqrt{67.96875} \approx 8.2443 $$

Rounding to three significant figures:

$$ v \approx 8.24\text{ m/s} $$

Answer:

8.24