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A 9,000 kg car moving at 8 m/s due east collides with a 12,000 kg SUV moving due west at 7m/s. After the collision, the 9,000 kg car moves due west at 6 m/s. Calculate the momentum of the SUV. Determine the speed of the SUV.

User Dancrumb
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ANSWER


\begin{gathered} 42,000\operatorname{kg}m\/s \\ 3.5m\/s\text{ due East} \end{gathered}

Step-by-step explanation

Parameters given:

Mass of car, m = 9,000 kg

Mass of SUV, M = 12,000 kg

Initial speed of car, u = 8 m/s (taking East to be the positive direction)

Initial speed of SUV, U = - 7 m/s (taking West to be the negative direction)

Final speed of car, v = -6 m/s

To find the final momentum of the SUV, we have to apply the principle of conservation of momentum, which states that:

This implies that:


p_(ic)+p_(is)=p_(fc)+p_(fs)

where pic = initial momentum of the car, pis = initial momentum of the SUV, pfc = final momentum of the car, pfs = final momentum of the SUV

We can rewrite the formula above as follows:


mu+MU=mv+MV

where MV represents the final momentum of the SUV.

Therefore, we have that the final momentum of the SUV is:


\begin{gathered} mu+MU=mv+p_(fs) \\ (9000\cdot8)+(12000\cdot(-7))=(9000\cdot-6)+p_(fs) \\ \Rightarrow72,000-84,000=-54,000+p_(fs) \\ \Rightarrow p_(fs)=72,000-84,000+54,000 \\ p_(fs)=42,000\operatorname{kg}m\/s \end{gathered}

To find the speed of the SUV after the collision, we have to find the final speed of the SUV.

We have that from the formula for momentum:


\begin{gathered} p_(fs)=M\cdot V \\ \Rightarrow V=(p_(fs))/(M) \end{gathered}

Therefore, the final speed of the SUV is:


\begin{gathered} V=(42,000)/(12,000) \\ V=3.5m\/s \end{gathered}

Since it is positive, the speed is due East.

User Brainray
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