4. Two vehicles of equal mass collide at a 90° degree intersection. If the momentum of vehicle A is 1.20x10^5 kg km/h east and the momentum of vehicle B is 8.50x10^4 kg km/h north, what is the resulting momentum of the final mass?
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The same as the original momentum.
To find the resulting momentum of the final mass after the collision, we need to use vector addition since the two vehicles are colliding at a 90° intersection.
First, let's convert the momenta of the vehicles into a common unit, such as kg m/s. To do this, we need to convert the given values from kg km/h to kg m/s.
1.20 × 10^5 kg km/h east:
To convert km/h to m/s, we need to multiply by a conversion factor of 1000/3600 since there are 1000 meters in a kilometer and 3600 seconds in an hour.
(1.20 × 10^5 kg km/h) × (1000 m/km) / (3600 s/h) = (1.20 × 10^5 kg) × (1000 m)/(3600 s)
Similarly, for 8.50 × 10^4 kg km/h north, we can use the same conversion factor:
(8.50 × 10^4 kg km/h) × (1000 m/km) / (3600 s/h) = (8.50 × 10^4 kg) × (1000 m)/(3600 s)
Now we have converted the momenta into kg m/s, let's proceed with vector addition.
Since the two vehicles collide at a 90° intersection, we can treat their momenta as perpendicular vector components. In this case, we can use the Pythagorean theorem to find the magnitude of the resultant momentum:
Resultant momentum = √((momentum of A)^2 + (momentum of B)^2)
Plugging in the values:
Resultant momentum = √((1.20 × 10^5 kg m/s)^2 + (8.50 × 10^4 kg m/s)^2)
Now we can calculate the value of the resultant momentum using a calculator:
Resultant momentum ≈ √((1.44 × 10^10) + (7.22 × 10^9)) kg m/s
Simplifying this expression gives us the magnitude of the resultant momentum of the final mass after the collision.