Please Help....

A car (mass = 1170 kg) is traveling at 43 m/s when it collides head-on with a sport utility vehicle (mass = 2460 kg) traveling in the opposite direction. In the collision, the two vehicles come to a halt. At what speed was the sport utility vehicle traveling?

change of momentum applies

intial momentum = final momentum
1170*43+2460(v)=0
solve for v

To solve this problem, we can use the principles of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision. Momentum is defined as the product of an object's mass and velocity.

Let's first find the momentum before the collision. The momentum of the car before the collision can be calculated using the formula:

Momentum of car before collision = Mass of car × Velocity of car

Momentum of car before collision = 1170 kg × 43 m/s
Momentum of car before collision = 50,310 kg·m/s

The momentum of the sport utility vehicle before the collision can be calculated similarly:

Momentum of SUV before collision = Mass of SUV × Velocity of SUV

Momentum of SUV before collision = 2460 kg × Velocity of SUV

Now, since the two vehicles are colliding head-on, the direction of momentum of the car is opposite to that of the SUV. So, we represent the car's momentum as negative:

Momentum of car after collision = - Mass of car × Velocity of car

And the momentum of the SUV after the collision is represented as positive:

Momentum of SUV after collision = Mass of SUV × Velocity of SUV

Since the total momentum is conserved:

Total momentum before collision = Total momentum after collision

Momentum of car before collision + Momentum of SUV before collision = Momentum of car after collision + Momentum of SUV after collision

Substituting the known values and applying the conservation of momentum principle:

50,310 kg·m/s + (2460 kg × Velocity of SUV) = - (1170 kg × 0 m/s) + (2460 kg × Velocity of SUV)

Now, let's solve this equation for the Velocity of SUV:

50,310 kg·m/s + (2460 kg × Velocity of SUV) = 0 + (2460 kg × Velocity of SUV)

Simplifying the equation:

50,310 kg·m/s = 2460 kg × Velocity of SUV

Dividing both sides by 2460 kg:

(50,310 kg·m/s) / 2460 kg = Velocity of SUV

The velocity of the SUV can be found by performing the division:

Velocity of SUV = 20.45 m/s

Therefore, the sport utility vehicle was traveling at a speed of approximately 20.45 m/s before the collision.