A 905 kg red car is travelling to the right with a speed of 2 m/s when it strikes a 1,496 kg travelling to the left at a speed of 5.3 m/s. After the collision, the yellow car travels to left at a speed of 0.9 m/s. What is the velocity of red car after the collision?

Question

BlackTom AI · Accepted Answer

We start by identifying the given data and choosing a sign convention. Let the rightward direction be positive for velocity. The red car (mass 905 kg) initially moves to the right at +2 m/s. The yellow car (mass 1496 kg) moves to the left at -5.3 m/s. After the collision, the yellow car moves to the left at -0.9 m/s, so the red car’s final velocity v_r’ is what we need to find.

Apply conservation of linear momentum: total momentum before collision equals total momentum after collision.
Initial momentum = (905)(+2) + (1496)(-5.3).
Compute: 905×2 = 1810. 1496×5.3 = 7928.8, so 1496×(-5.3) = -7928.8. Therefore initial momentum = 1810 - 7928.8 = -6118.8 kg·m/s.
Final momentum = (905)(v_r’) + (1496)(-0.9) = 905v_r’ - 1346.4.
Set initial equal to final:
-6118.8 = 905v_r’ - 1346.4.
Solve for v_r’: add 1346.4 to both sides to isolate the term with v_r’, giving -6118.8 + 1346.4 = 905v_r’, which is -4772.4 = 905v_r’. Divide both sides by 905: v_r’ = -4772.4 / 905 ≈ -5.2735 m/s.

Thus, the red car’s velocity after the collision is about -5.27 m/s, indicating it moves to the left with that speed. The negative sign reflects the chosen positive direction (to the right). The calculation is consistent with momentum conservation, given both masses and the final velocity of the yellow car. The intermediate arithmetic steps (momenta products and the final division) support this result. Any small rounding in intermediate steps still yields a final value near -5.27 m/s.

A 905 kg red car is travelling to the right with a speed of 2 m/s when it strikes a 1,496 kg travelling to the left at a speed of 5.3 m/s. After the collision, the yellow car travels to left at a speed of 0.9 m/s. What is the velocity of red car after the collision?简答题

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