Question

Two vehicles A (mass 520kg) and B (1.7 tons) collide at an intersection. Before the collision, vehicle A traveled at a velocity of 120km/h in an eastern direction and vehicle B traveled with a velocity of 85km/h in a northern direction. The collision is in elastic.
1. Calculate the momentum of Vehicle A before the collision (magnitude only).
2. Calculate the momentum of vehicle B before the collision (magnitude only).
3. Calculate the momentum before the collision (magnitude only).

Answer 1

By definition, the momentum is:

$$p = mv$$

where $m$ is the mass and $v$ is the speed of a vehicle.

1.  The momentum of Vehicle A before the collision

$$p_A = m_Av_A = 520kg\cdot 120 km/h = 520kg\cdot 33.(3)m/s \approx 17333 kg\cdot m/s$$

2.  The momentum of Vehicle B before the collision

$$p_B = m_Bv_B = 1.7\space tons \cdot 85\space km/h = 1700kg\cdot 23.6(1)m/s \approx 40139 kg\cdot m/s$$

3.  The momentum before the collision

As far as $p_A$ and $p_B$ are perpendicular to each other, the magnitude of their sum can be found using the Pythagorean theorem:

$$p = \sqrt{p_A^2 + p_B^2} =\sqrt{17333^2 + 40139^2}\approx 43722kg\cdot m/s$$

Answer. 1. 17333 kg*m/s, 2. 40139 kg*m/s, 3. 43722 kg*m/s.