Two cars collide at an intersection. Car A𝐴, with a mass of 2000 kgkg, is going from west to east, while car B𝐵, of mass 1500 kgkg, is going from north to south at 17 m/sm/s. As a result of this collision, the two cars become enmeshed and move as one afterwards. In your role as an expert witness, you inspect the scene and determine that, after the collision, the enmeshed cars moved at an angle of 55 ∘∘ south of east from the point of impact.Part AHow fast were the enmeshed cars moving just after the collision?Express your answer in meters per second.Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typev𝑣 =nothingm/sm/sSubmitRequest AnswerPart BHow fast was car A𝐴 going just before the collision?Express your answer in meters per second.Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typevA𝑣𝐴 =nothing
Question
Two cars collide at an intersection. Car A𝐴, with a mass of 2000 kgkg, is going from west to east, while car B𝐵, of mass 1500 kgkg, is going from north to south at 17 m/sm/s. As a result of this collision, the two cars become enmeshed and move as one afterwards. In your role as an expert witness, you inspect the scene and determine that, after the collision, the enmeshed cars moved at an angle of 55 ∘∘ south of east from the point of impact.Part AHow fast were the enmeshed cars moving just after the collision?Express your answer in meters per second.Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typev𝑣 =nothingm/sm/sSubmitRequest AnswerPart BHow fast was car A𝐴 going just before the collision?Express your answer in meters per second.Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typevA𝑣𝐴 =nothing
Solution
This problem involves the conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.
Part A:
Let's denote the velocity of the enmeshed cars as v, the velocity of car A as vA, and the velocity of car B as vB. The mass of car A is mA = 2000 kg, and the mass of car B is mB = 1500 kg.
The momentum of car A before the collision is mAvA, and the momentum of car B before the collision is mBvB. The total momentum before the collision is mAvA + mBvB.
The momentum of the enmeshed cars after the collision is (mA+mB)*v. According to the conservation of momentum, we have:
mAvA + mBvB = (mA+mB)*v
We know that car B was moving at 17 m/s, so we can substitute vB = 17 m/s into the equation:
mAvA + mB17 = (mA+mB)*v
We also know that the enmeshed cars moved at an angle of 55 degrees south of east, which means that the velocity v can be decomposed into two components: vcos(55) in the east direction (the same direction as car A), and vsin(55) in the south direction (the same direction as car B). Therefore, we can write two equations:
mAvA = mAvcos(55) mB17 = mBvsin(55)
Solving these two equations, we can find the velocity v of the enmeshed cars just after the collision.
Part B:
Once we have found the velocity v, we can substitute it back into the equation mAvA = mAv*cos(55) to find the velocity vA of car A just before the collision.
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