A car (mass = 1150 kg) is traveling at 32 m/s when it collides head-on with a sport utility vehicle (mass = 2550 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?
momentum is conserved. If the end momentum is zero, the initial momentum was zero.
1150*32-2550v=0
solve for v.
To solve this problem, 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 can be calculated by multiplying its mass by its velocity. Mathematically, momentum (p) is given by:
p = mass x velocity
For the car, before the collision, the momentum is given by:
p_car_before_collision = mass_car x velocity_car
After the collision, both vehicles come to a halt, so their final velocities are zero:
p_car_after_collision = mass_car x velocity_car_after_collision = 0
For the sport utility vehicle (SUV), the momentum before the collision is:
p_SUV_before_collision = mass_SUV x velocity_SUV
After the collision, the SUV comes to a halt, so its final velocity is also zero:
p_SUV_after_collision = mass_SUV x velocity_SUV_after_collision = 0
According to the conservation of momentum principle, the total momentum before the collision is equal to the total momentum after the collision:
p_car_before_collision + p_SUV_before_collision = p_car_after_collision + p_SUV_after_collision
Since the final velocities are zero for both vehicles, the equation becomes:
p_car_before_collision + p_SUV_before_collision = 0
Substituting the momentum equations for the car and SUV before the collision:
mass_car x velocity_car + mass_SUV x velocity_SUV = 0
Given that the mass of the car (m_car) is 1150 kg and the mass of the SUV (m_SUV) is 2550 kg, and the car's velocity (v_car) is 32 m/s, we can solve for the SUV's velocity (v_SUV):
1150 kg x 32 m/s + 2550 kg x v_SUV = 0
36800 kg·m/s + 2550 kg·v_SUV = 0
2550 kg·v_SUV = -36800 kg·m/s
v_SUV = (-36800 kg·m/s) / 2550 kg
v_SUV ≈ -14.39 m/s
Therefore, the speed of the SUV before the collision was approximately 14.39 m/s in the opposite direction of the car.