a 2400kg vehicle travelling north at 10.0m/s collides with a 500kg vehicle that is travelling east at 20.0m/s if the 2 vehicles lock together, what is their speed just after the collision

To find the speed of the two vehicles just after the collision, we can use the principle of conservation of momentum.

The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act upon it. In this case, we can assume that there are no external forces acting on the system of the two vehicles.

Momentum (p) is defined as the product of an object's mass (m) and its velocity (v). The equation for momentum is:

p = m * v

Now, let's consider the momentum of the northbound vehicle before the collision. Since it is only moving in the north direction, its momentum can be calculated as:

p1 = m1 * v1

where m1 is the mass of the northbound vehicle and v1 is its velocity.

Similarly, the momentum of the eastbound vehicle before the collision can be calculated as:

p2 = m2 * v2

where m2 is the mass of the eastbound vehicle and v2 is its velocity.

The total momentum of the system before the collision can be calculated by adding the individual momenta of the two vehicles:

p_total = p1 + p2

Now, since the two vehicles lock together after the collision, they become a single system. The total mass of the system after the collision is the sum of the masses of the two vehicles:

m_total = m1 + m2

Finally, we can calculate the velocity of the two vehicles just after the collision by dividing the total momentum of the system after the collision by its total mass:

v_total = p_total / m_total

Substituting the given values:

m1 = 2400 kg (mass of the northbound vehicle)
v1 = 10.0 m/s (velocity of the northbound vehicle)
m2 = 500 kg (mass of the eastbound vehicle)
v2 = 20.0 m/s (velocity of the eastbound vehicle)

Let's calculate the individual momenta:

p1 = 2400 kg * 10.0 m/s = 24000 kg*m/s
p2 = 500 kg * 20.0 m/s = 10000 kg*m/s

Then, calculate the total momentum of the system before the collision:

p_total = p1 + p2 = 24000 kg*m/s + 10000 kg*m/s
= 34000 kg*m/s

Calculate the total mass of the system after the collision:

m_total = m1 + m2 = 2400 kg + 500 kg
= 2900 kg

Finally, calculate the velocity of the two vehicles just after the collision:

v_total = p_total / m_total = 34000 kg*m/s / 2900 kg
≈ 11.72 m/s

Therefore, the speed of the two vehicles just after the collision is approximately 11.72 m/s.