23 What is the kinetic energy of a 13 kg dog that is running at a speed of \( 8.5 \mathrm{~m} / \mathrm{s} \) ?

To find the kinetic energy of the dog, we can use the formula for kinetic energy: \[ \text{Kinetic Energy} = \frac{1}{2} \times \text{mass} \times \text{velocity}^2 \] Given: - Mass of the dog = 13 kg - Velocity of the dog = 8.5 m/s Substitute the values into the formula: \[ \text{Kinetic Energy} = \frac{1}{2} \times 13 \times (8.5)^2 \] Now, we can calculate the kinetic energy. Calculate the value by following steps: - step0: Calculate: \(\frac{1}{2}\times 13\times 8.5^{2}\) - step1: Convert the expressions: \(\frac{1}{2}\times 13\left(\frac{17}{2}\right)^{2}\) - step2: Multiply the terms: \(\frac{13}{2}\left(\frac{17}{2}\right)^{2}\) - step3: Evaluate the power: \(\frac{13}{2}\times \frac{17^{2}}{2^{2}}\) - step4: Multiply the fractions: \(\frac{13\times 17^{2}}{2\times 2^{2}}\) - step5: Multiply: \(\frac{3757}{2^{3}}\) - step6: Evaluate the power: \(\frac{3757}{8}\) The kinetic energy of the 13 kg dog running at a speed of 8.5 m/s is approximately 469.625 joules.