Formula 1 point A 107 kg box falls from a plane and hit's the ground at \( 16 \mathrm{~km} / \mathrm{h} \). How many Joules of kinetic energy does the box have when it hits the ground?

To find the kinetic energy of the box when it hits the ground, 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 box = 107 kg - Velocity of the box when it hits the ground = 16 km/h First, we need to convert the velocity from km/h to m/s: \[ \text{Velocity in m/s} = \frac{16 \times 1000}{3600} \] Now, we can calculate the kinetic energy using the formula. Calculate the value by following steps: - step0: Calculate: \(\frac{1}{2}\times 107\left(\frac{16\times 1000}{3600}\right)^{2}\) - step1: Reduce the fraction: \(\frac{1}{2}\times 107\left(\frac{40}{9}\right)^{2}\) - step2: Multiply the terms: \(\frac{107}{2}\left(\frac{40}{9}\right)^{2}\) - step3: Evaluate the power: \(\frac{107}{2}\times \frac{40^{2}}{9^{2}}\) - step4: Rewrite the expression: \(\frac{107}{2}\times \frac{8^{2}\times 5^{2}}{9^{2}}\) - step5: Rewrite the expression: \(\frac{107}{2}\times \frac{2^{6}\times 5^{2}}{9^{2}}\) - step6: Reduce the numbers: \(107\times \frac{2^{5}\times 5^{2}}{9^{2}}\) - step7: Multiply: \(\frac{107\times 800}{9^{2}}\) - step8: Multiply: \(\frac{85600}{9^{2}}\) - step9: Evaluate the power: \(\frac{85600}{81}\) The box has approximately 1056.79 Joules of kinetic energy when it hits the ground.