A 3250kg truck traveling 44m/s north collides with a 1500kg car traveling 17m/s south. If the two vehicles stick together after the collision, what is the speed and direction of the two vehicles?

M1*V1 + M2*V2 = M1V + M2*V.

3250*44 - 1500*17 = 3250V + 1500V.
V = ?
Direction: North.

To find the speed and direction of the two vehicles after the collision, we need to apply the law of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.

Momentum is calculated by multiplying the mass of an object by its velocity. Since the truck is traveling north and the car is traveling south, we'll assign the positive direction to the north and the negative direction to the south.

Before the collision, the momentum of the truck (m1) is given by:
m1 = mass of the truck × velocity of the truck
= 3250 kg × 44 m/s (north)
= +143,000 kg·m/s (north) (The positive sign indicates the north direction)

Similarly, the momentum of the car (m2) is given by:
m2 = mass of the car × velocity of the car
= 1500 kg × 17 m/s (south)
= -25,500 kg·m/s (south) (The negative sign indicates the south direction)

Now, for the total momentum before the collision:
total momentum before the collision = m1 + m2
= +143,000 kg·m/s (north) + (-25,500 kg·m/s) (south)

Since the vehicles stick together after the collision, their total momentum after the collision should be zero (no external forces acting on them).

So, the total momentum after the collision will be:
total momentum after the collision = 0

Now, we can calculate the speed and direction of the two vehicles after the collision.

Let's assume that the velocity of the combined trucks is V (unknown) and in the north direction. The momentum of the trucks after the collision (m1') is given by:
m1' = (m1 + m2') (since the two vehicles stick together)
= (3250 kg + 1500 kg) kg × V m/s
= 4750 kg × V m/s (north)

Since the total momentum after the collision is zero, we have:
m1' = 0
4750 kg × V m/s (north) = 0

Solving the equation for V, we get:
V = 0 m/s (north)

Therefore, the speed of the two vehicles after the collision is 0 m/s, and their direction is in the north direction. This means that the combined vehicles come to a complete stop.