A car (mass = 1100 kg) is traveling at 33.0 m/s when it collides head-on with a sport utility vehicle (mass = 2800 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?
final momentum=0, so sum of vehicles' momenta is 0.
1100*33 + 2800*v = 0
36300 = -2800v
v = -12.96
speed is just 12.96 m/s
To find the speed of the sport utility vehicle, we can use the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of a system of objects remains constant if no external forces are acting on it.
In this case, the initial momentum of the car is equal to the final momentum of the car and sport utility vehicle together.
The momentum of an object is given by the product of its mass and velocity.
The initial momentum of the car is calculated by multiplying its mass (1100 kg) by its initial velocity (33.0 m/s), which gives us 36,300 kg⋅m/s.
After the collision, both vehicles come to a halt, so their final velocity is 0 m/s.
The momentum of the sport utility vehicle is calculated by multiplying its mass (2800 kg) by its final velocity, which is the value we're trying to find.
Thus, we can set up the equation:
Initial momentum of the car = Final momentum of the car + Final momentum of the sport utility vehicle
(1100 kg) * (33.0 m/s) = (0 kg) * (0 m/s) + (2800 kg) * (v)
36,300 kg⋅m/s = 0 kg⋅m/s + 2800 kg * v
Simplifying the equation, we can solve for v (the velocity of the sport utility vehicle):
36,300 kg⋅m/s = 2800 kg * v
Dividing both sides of the equation by 2800 kg, we get:
v = 36,300 kg⋅m/s / 2800 kg
v ≈ 13 m/s
Therefore, the sport utility vehicle was traveling at approximately 13 m/s before the collision.