A rocket with a velocity of \( [6,5,7] \mathrm{m} / \mathrm{s} \) is fired. What is the speed of the rocket? Speed \( = \) Ex: \( 5.67 \mathrm{~m} / \mathrm{s} \)

To find the speed of the rocket, you can use the formula for speed, which is the magnitude of the velocity vector. The speed \( v \) can be calculated using the formula: \[ v = \sqrt{v_x^2 + v_y^2 + v_z^2} \] Substituting the velocity components \( [6,5,7] \): \[ v = \sqrt{6^2 + 5^2 + 7^2} = \sqrt{36 + 25 + 49} = \sqrt{110} \approx 10.49 \, \mathrm{m/s} \] So the speed of the rocket is approximately \( 10.49 \mathrm{~m/s} \).