How can we determine the magnitude of the resulting momentum when two pickup trucks crash at a 90∘ intersection?
The resulting momentum of the collision at a 90 degree angle can be calculated using the principle of conservation of momentum and the Pythagorean theorem. The magnitude of the final momentum is approximately 7.77×10^4 kg km/h.
Principle of Conservation of Momentum
The principle of conservation of momentum states that the total momentum of an isolated system remains constant before and after a collision. This means that the total momentum of the two pickup trucks before the collision is equal to the total momentum after the collision.
Pythagorean Theorem
In this case, the two pickup trucks are colliding at a 90 degrees angle. Since their momenta are perpendicular to each other, we can use the Pythagorean theorem to calculate the resultant momentum. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Calculation
Using the Pythagorean theorem, we can calculate the magnitude of the final momentum as the square root of the sum of the squares of both momenta involved:
√((4.60×10^4)^2 + (6.25×10^4)^2)
After performing the calculation, we get:
√((4.60×10^4)^2 + (6.25×10^4)^2) = √(21.16×10^8 + 39.06×10^8) = √60.22×10^8 = 7.77×10^4 kg km/h
Therefore, the magnitude of the resulting momentum after the collision of the two pickup trucks at a 90 degrees intersection is approximately 7.77×10^4 kg km/h.