Question

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.

Answer 1

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:

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.