a.
The direction of the total momentum is 45°
The momentum of the first car is given by p = mv where m = mass of car = 1200 kg and v = velocity of car = 15 m/sj (since it moves due north).
So, p = mv
= 1200 kg × (15 m/s)j
= (18000 kgm/s)j
Also, the momentum of the identical car, p' = mv' where m = mass of car = 1200 kg and v' = velocity of car = (15 m/s)i (since it moves due east).
So, p' = mv'
= 1200 kg × (15 m/s)i
= (18000 kgm/s)i
So, the total momentum of the system P = p + p'
= (18000 kgm/s)j + (18000 kgm/s)i
= (18000 kgm/s)i + (18000 kgm/s)j
The direction of the total momentum of the system P is gotten from
tanФ = p'/p
= 18000 kgm/s ÷ 18000 kgm/s
= 1
Ф = tan⁻¹(1)
= 45°
The direction of the total momentum is 45°
b.
The magnitude of the total momentum of the system is 25455.84 kgm/s
The magnitude of the total momentum of the system P = √(p'² + p²)
= √[(18000 kgm/s)² + (18000 kgm/s)²]
= (18000 kgm/s)√(1 + 1)
= (18000 kgm/s)√2
= 25455.84 kgm/s
The magnitude of the total momentum of the system is 25455.84 kgm/s
Learn more about total momentum here:
https://brainly.com/question/25635296
