A car (mass = 1180 kg) is traveling at 36 m/s when it collides head-on with a sport utility vehicle (mass = 2380 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?

If the collided vehicles both come to a stop (stuck together), the initial momenta must be equal and opposite.

To find the speed of the sport utility vehicle (SUV) before the collision, we can apply the principle of conservation of momentum.

The principle of conservation of momentum states that the total momentum of a system remains constant unless acted upon by external forces. In this case, the external force causing the vehicles to come to a halt is the collision.

The momentum of an object is given by the product of its mass and velocity. Mathematically, momentum (p) can be calculated using the formula:

p = m × v

where p is momentum, m is mass, and v is velocity.

According to the conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision. Since the car and SUV come to a halt, their final momentum is zero.

Let's represent the velocity of the car as v_car and the velocity of the SUV as v_suv.

Before the collision, the car has a mass of 1180 kg and a velocity of 36 m/s. Therefore, the momentum of the car (p_car) is:

p_car = 1180 kg × 36 m/s

After the collision, both the car and the SUV come to a halt, so their final velocities are zero. This means that the momenta of the car and the SUV after the collision are both zero:

p_car_after = 0
p_suv_after = 0

According to the principle of conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision. Thus, we can set up the equation:

p_car_before + p_suv_before = p_car_after + p_suv_after

Substituting the known values, we get:

(1180 kg × 36 m/s) + (2380 kg × v_suv) = 0

Now we can solve for v_suv, which is the velocity of the SUV before the collision. Rearranging the equation, we have:

(1180 kg × 36 m/s) = - (2380 kg × v_suv)

Dividing both sides by 2380 kg, we get:

v_suv = (1180 kg × 36 m/s) / 2380 kg

Simplifying this equation, we find:

v_suv = 16.9 m/s

Therefore, the sport utility vehicle was traveling at a speed of 16.9 m/s before the collision.