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Transcribed Image Text:**Problem Statement:**
A 10.0 kg toy car moves along an x-axis with a velocity given by \( \vec{v} = -7.89t^3 \hat{\imath} \, \text{m/s} \), with \( t \) in seconds. For \( t > 0 \), calculate:
- (a) the angular momentum \( \vec{L} \) of the car about the origin.
- (b) the torque \( \vec{\tau} \) on the car about the origin.
Calculations are also required for:
- (c) \( \vec{L} \) about the point (5.92 m, 6.76 m, 0).
- (d) \( \vec{\tau} \) about the point (5.92 m, 6.76 m, 0).
- (e) \( \vec{L} \) about the point (5.92 m, -6.76 m, 0).
- (f) \( \vec{\tau} \) about the point (5.92 m, -6.76 m, 0).
**Calculation Template:**
For each of the above calculations, fill in the appropriate values into the expressions below:
- \((a)\) \( \left( \_\_\_ \right) \hat{\jmath} + \left( \_\_\_ \right) \hat{k} \)
- \((b)\) \( \left( \_\_\_ \right) \hat{\imath} + \left( \_\_\_ \right) \hat{k} \)
- \((c)\) \( \left( \_\_\_ \right) \hat{\imath} + \left( \_\_\_ \right) \hat{k} \cdot t^3 \)
- \((d)\) \( \left( \_\_\_ \right) \hat{\imath} + \left( \_\_\_ \right) \hat{k} \cdot t^2 \)
- \((e)\) \( \left( \_\_\_ \right) \hat{\imath} + \left( \_\_\_ \right) \hat{k} \cdot t^3 \)
- \((f)\) \( \left( \_\_\_ \right) \hat
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