A car (mass = 1070 kg) is traveling at 40 m/s when it collides head-on with a sport utility vehicle (mass = 2570 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 they come to a halt, then the total momentum is zero, and since it was conserved, the original momenum was zero.
MV+mv=0
V=-mv/M
To find the speed of the sport utility vehicle (SUV) before the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is calculated by multiplying its mass by its velocity:
momentum = mass × velocity
Before the collision, the momentum of the car is given by:
momentum of car = mass of car × velocity of car
After the collision, both vehicles come to a halt, so their final velocities are zero. Therefore, the momentum of both vehicles after the collision is zero.
Using the conservation of momentum principle, we can write:
momentum before collision = momentum after collision
(mass of car × velocity of car) + (mass of SUV × velocity of SUV) = 0
Substituting the given values:
(1070 kg × 40 m/s) + (2570 kg × velocity of SUV) = 0
Simplifying the equation:
42800 kg·m/s + (2570 kg × velocity of SUV) = 0
To solve for the velocity of the SUV, isolate the variable:
2570 kg × velocity of SUV = -42800 kg·m/s
velocity of SUV = (-42800 kg·m/s) / 2570 kg
velocity of SUV ≈ -16.67 m/s
Since speed is always positive, we take the absolute value of the result:
speed of SUV = |-16.67 m/s| ≈ 16.67 m/s
Therefore, the sport utility vehicle (SUV) was traveling at approximately 16.67 m/s before the collision.