Understanding Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion. The amount of kinetic energy depends on the object's mass and its speed.

Kinetic Energy Formula

The formula used to calculate kinetic energy (KE) is:

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

Where:

• $KE$ is the kinetic energy (measured in Joules, J)
• $m$ is the mass of the object (measured in kilograms, kg)
• $v$ is the speed of the object (measured in meters per second, m/s)

Applying the Formula to the Cricket Ball

We are given the following information:

• Mass of the cricket ball, $m = 160$ g
• Speed of the cricket ball, $v = 22$ m/s

First, we need to convert the mass from grams (g) to kilograms (kg) because the standard unit for mass in the kinetic energy formula is kilograms.

$$ 1 \text{ kg} = 1000 \text{ g} $$

So, the mass in kilograms is:

$$ m = \frac{160 \text{ g}}{1000 \text{ g/kg}} = 0.160 \text{ kg} $$

Calculation Steps

Now, we can substitute the values into the kinetic energy formula:

$$ KE = \frac{1}{2} \times m \times v^2 $$

$$ KE = \frac{1}{2} \times 0.160 \text{ kg} \times (22 \text{ m/s})^2 $$

Calculate the square of the speed:

$$ (22 \text{ m/s})^2 = 484 \text{ m}^2/\text{s}^2 $$

Now, multiply the values:

$$ KE = 0.5 \times 0.160 \text{ kg} \times 484 \text{ m}^2/\text{s}^2 $$

$$ KE = 0.080 \text{ kg} \times 484 \text{ m}^2/\text{s}^2 $$

$$ KE = 38.72 \text{ kg} \cdot \text{m}^2/\text{s}^2 $$

Since $1 \text{ Joule (J)} = 1 \text{ kg} \cdot \text{m}^2/\text{s}^2$, the kinetic energy is:

$$ KE = 38.72 \text{ J} $$

Final Answer

The kinetic energy of the cricket ball is 38.72 Joules. This matches option 4.