The initial velocity of a particle of mass 0.1kg is 40 m/s in the direction of the unit vector j. The velocity of the particle changed to 30 m/s in the dire...
Question 1 Report
The initial velocity of a particle of mass 0.1kg is 40 m/s in the direction of the unit vector j. The velocity of the particle changed to 30 m/s in the direction of the unit vector i. Find the change in momentum.
Answer Details
Momentum \( = \text{mass} \times \text{velocity} \), and change in momentum \( = m(\vec{v}_f - \vec{v}_i) \).
Initial velocity: \( \vec{v}_i = 40\mathbf{j} \); final velocity: \( \vec{v}_f = 30\mathbf{i} \); mass \( m = 0.1\text{ kg} \).
\[ \Delta \vec{p} = 0.1(30\mathbf{i} - 40\mathbf{j}) = (3\mathbf{i} - 4\mathbf{j})\text{ kg ms}^{-1}. \]
Magnitude: \[ |\Delta \vec{p}| = \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = 5\text{ kg ms}^{-1}. \]
The change in momentum is \( 3\mathbf{i} - 4\mathbf{j} \) (magnitude \(5\text{ kg ms}^{-1}\)).
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