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# Ask AI: A 1.66 kg particle has a velocity of vx = 2.76 m/s and vy = 7.11 m/s. Find the magnitude of its total momentum.

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Question: A 1.66 kg particle has a velocity of vx = 2.76 m/s and vy = 7.11 m/s. Find the magnitude of its total momentum.

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The total momentum (p) of a particle is given by the product of its mass (m) and velocity (v). The velocity in this case is a vector quantity as it has both magnitude and direction, given as vx and vy. First, we need to find the net velocity (v) which is the hypotenuse of the right triangle formed by velocities vx and vy, then we can use it to get the total momentum. The magnitude of the velocity vector is calculated using the Pythagorean theorem: v = sqrt(vx² + vy²). So, first calculate v: v = sqrt((2.76 m/s)² + (7.11 m/s)²) v ≈ 7.50 m/s (after calculating and rounding to two decimal places) Then we can calculate the total momentum: p = m * v p = 1.66 kg * 7.50 m/s p ≈ 12.45 kg*m/s (after calculating and rounding to two decimal places) So the magnitude of its total momentum is approximately 12.45 kg*m/s.

Dec. 8, 2023, 8:16 a.m.

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