A 1000 kg car sliding on frictionless ice at 22 m/s hits a stationary 2500 kg minivan. The two vehicles are locked together after impact on the ice. What is their speed after impact?
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
Before the collision, the car's momentum is given by:
momentum_car_before = mass_car * velocity_car
momentum_car_before = 1000 kg * 22 m/s = 22000 kg·m/s
The minivan is stationary before the collision, so its momentum is zero:
momentum_minivan_before = mass_minivan * velocity_minivan
momentum_minivan_before = 2500 kg * 0 m/s = 0 kg·m/s
The total momentum before the collision is the sum of the momenta of the car and the minivan:
total_momentum_before = momentum_car_before + momentum_minivan_before
total_momentum_before = 22000 kg·m/s + 0 kg·m/s = 22000 kg·m/s
After the collision, the two vehicles are locked together and move as a single unit. Let's suppose their combined speed after the collision is v.
The total momentum after the collision is the sum of the momenta of the car and the minivan:
total_momentum_after = (mass_car + mass_minivan) * v
total_momentum_after = (1000 kg + 2500 kg) * v = 3500 kg * v
According to the conservation of momentum principle, the total momentum before the collision should be equal to the total momentum after the collision:
total_momentum_before = total_momentum_after
22000 kg·m/s = 3500 kg * v
Solving for v, we can determine the speed of the combined vehicles after the collision:
v = 22000 kg·m/s / 3500 kg
v = 6.28 m/s
Therefore, the speed of the car and minivan combined after the impact is approximately 6.28 m/s.