If a 0.0500 kg projectile is launched with a velocity of 2.7 m/s, what is the kinetic energy of the projectile?

Steps to Solve

1. Identify the given values First, identify the mass ($m$) and velocity ($v$) of the projectile. For this example, let's say the mass is 2 kg and the velocity is 10 m/s.

2. Substitute the values into the kinetic energy formula Use the kinetic energy formula $KE = 0.5 \times m \times v^2$. Substitute the identified values into the formula:

$$ KE = 0.5 \times 2 , \text{kg} \times (10 , \text{m/s})^2 $$

3. Calculate the square of the velocity Calculate $v^2$, which is $(10 , \text{m/s})^2$:

$$ (10 , \text{m/s})^2 = 100 , \text{m}^2/\text{s}^2 $$

4. Complete the kinetic energy calculation Insert the calculated value of $v^2$ into the kinetic energy formula:

$$ KE = 0.5 \times 2 , \text{kg} \times 100 , \text{m}^2/\text{s}^2 $$

5. Multiply to find the kinetic energy Finally, perform the multiplication:

$$ KE = 0.5 \times 200 , \text{kg} \cdot \text{m}^2/\text{s}^2 = 100 , \text{J} $$