A car (mass=1100kg) is traveling at 32m/s when it collides head on with a sport utility vehicle (mass=2500kg) traveling in the opposite direction. In the collision, the two vehicles come to a halt. at what speed was the sport utility vehicle traveling.
momentumcar+momentumSUV=0
To find the speed at which the sport utility vehicle (SUV) was traveling before the collision, we can use 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 are acting on the system.
In this case, we can set up the equation as follows:
Total initial momentum = Total final momentum
For the initial momentum, we know that only the car is moving in the positive direction, so its momentum is given by:
Initial momentum of the car = mass of the car * velocity of the car = 1100 kg * 32 m/s
Since the SUV is traveling in the opposite direction, its velocity would be negative, so its momentum is given by:
Initial momentum of the SUV = mass of the SUV * (−velocity of the SUV) = 2500 kg * (−v) (where v is the velocity of the SUV)
After the collision, both vehicles come to a halt, so their final momentum is zero.
Set up the equation:
1100 kg * 32 m/s + 2500 kg * (−v) = 0
Solving for v:
1100 kg * 32 m/s − 2500 kg * v = 0
35200 kg·m/s − 2500 kg * v = 0
2500 kg * v = 35200 kg·m/s
v = 35200 kg·m/s / 2500 kg
v ≈ 14.08 m/s
Therefore, the sport utility vehicle was traveling at a speed of approximately 14.08 m/s before the collision.