A 2.91 kg particle has a velocity of (3.08 i - 3.95 j) m/s. (a) Find its x and y components of momentum. P, =8.608 Your response is vwithin 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. kg-m/s P. =-11.4045 v kg-m/s (b) Find the magnitude and direction of its momentum. 20.043 Your response differs from the correct answer by more than 10%. Double check your calculations. kg m/s 309.84 x °(clockwise from the +x axis)

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**Problem Statement:**

A 2.91 kg particle has a velocity of \( (3.08 \, \mathbf{i} - 3.35 \, \mathbf{j}) \, \text{m/s} \).

**Task:**

(a) Find its x and y components of momentum.

- \( p_x = 8.968 \) ❌ 
  - *Feedback:* Your response is within 10% of the correct value. This may be due to round-off error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize round-off error. (Answer in \(\text{kg m/s}\))

- \( p_y = -11.4945 \) ✔️ \(\, \text{kg m/s}\)

(b) Find the magnitude and direction of its momentum.

- Magnitude: \( 20.643 \) ❌ 
  - *Feedback:* Your response differs from the correct answer by more than 10%. Double check your calculations. (Answer in \(\text{kg m/s}\))

- Direction: \( 308.84^\circ \) ❌ (clockwise from the +x axis)

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**Explanation:**

In part (a), the components of momentum are calculated using the formula \( p = mv \), where \( m \) is mass and \( v \) is velocity. Each component should be calculated separately for the directions \( \mathbf{i} \) (x-axis) and \( \mathbf{j} \) (y-axis).

In part (b), the magnitude of momentum is derived using the Pythagorean theorem on the components, and the direction uses the arctangent function to find the angle relative to the positive x-axis. Errors should be checked for precision and accuracy by ensuring all calculations use sufficient significant figures.
Transcribed Image Text:**Problem Statement:** A 2.91 kg particle has a velocity of \( (3.08 \, \mathbf{i} - 3.35 \, \mathbf{j}) \, \text{m/s} \). **Task:** (a) Find its x and y components of momentum. - \( p_x = 8.968 \) ❌ - *Feedback:* Your response is within 10% of the correct value. This may be due to round-off error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize round-off error. (Answer in \(\text{kg m/s}\)) - \( p_y = -11.4945 \) ✔️ \(\, \text{kg m/s}\) (b) Find the magnitude and direction of its momentum. - Magnitude: \( 20.643 \) ❌ - *Feedback:* Your response differs from the correct answer by more than 10%. Double check your calculations. (Answer in \(\text{kg m/s}\)) - Direction: \( 308.84^\circ \) ❌ (clockwise from the +x axis) --- **Explanation:** In part (a), the components of momentum are calculated using the formula \( p = mv \), where \( m \) is mass and \( v \) is velocity. Each component should be calculated separately for the directions \( \mathbf{i} \) (x-axis) and \( \mathbf{j} \) (y-axis). In part (b), the magnitude of momentum is derived using the Pythagorean theorem on the components, and the direction uses the arctangent function to find the angle relative to the positive x-axis. Errors should be checked for precision and accuracy by ensuring all calculations use sufficient significant figures.
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