A car (mass = 1150 kg) is traveling at 26.7 m/s when it collides head-on with a sport utility vehicle (mass = 2030 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?

Include units.

m₁v-m₂u=0

u= m₁v/m₂=
=1150•26.7/2030=15.13 m/s

To determine the speed at which the sport utility vehicle was traveling before the collision, we need to apply the principle of conservation of momentum.

The principle of conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision, assuming no external forces act on the system.

The momentum of an object is defined as the product of its mass and velocity. Mathematically, momentum (p) is given by the equation:

p = m * v

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

In this case, we have a head-on collision, so the momentum of the car and sport utility vehicle are opposite in direction.

Before the collision, the momentum of the car is given by:
momentum_car_before = mass_car * velocity_car

After the collision, both vehicles come to a halt, so their final velocities are 0. Therefore, the momentum after the collision is 0 for both vehicles.

The total momentum before the collision is equal to the total momentum after the collision, so:

momentum_car_before + momentum_suv_before = 0

Substituting the values given:

mass_car * velocity_car + mass_suv * velocity_suv = 0

Solving for the velocity of the sport utility vehicle (velocity_suv):

velocity_suv = - (mass_car / mass_suv) * velocity_car

Substituting the given values:

mass_car = 1150 kg
mass_suv = 2030 kg
velocity_car = 26.7 m/s

Plugging them into the equation:

velocity_suv = - (1150 kg / 2030 kg) * 26.7 m/s

Calculating the velocity:

velocity_suv = - 0.566 * 26.7 m/s

Therefore, the speed at which the sport utility vehicle was traveling before the collision is approximately -15.117 m/s. The negative sign indicates that the direction is opposite to that of the car.