A northbound 3000 kg truck collides with an eastbound 2000 kg car. The two vehicles slide together as a single mangled object after the collision, and the direction of the slide is exactly northeast (45 degree angle between north and east). Which vehicle was going faster before the collision? How can you tell?
if velocity had been the same, then the angle N of E would be arctanTheta=3/2
which is 56 degrees. It was at 45 degrees, which means the Eastbound was the higher velociyt.
The lighter one had to be going faster.
To be at 45 degrees, momentum north = momentum east
2000 v = 3000 (2v/3)
To determine which vehicle was going faster before the collision, you can analyze the concept of momentum conservation. According to Newton's third law, the total momentum before the collision should be equal to the total momentum after the collision if no external forces are at play.
The momentum of an object can be calculated by multiplying its mass with its velocity. Let's assign the following variables:
- Mass of the truck (T) = 3000 kg
- Mass of the car (C) = 2000 kg
- Velocity of the truck before collision (Vt)
- Velocity of the car before collision (Vc)
After the collision, the single mangled object slides with a velocity in the northeast direction. Let's assume the velocity of the mangled object after the collision is (Vm).
To determine which vehicle was going faster before the collision, we need to compare their initial velocities. We can use the conservation of momentum equation:
(T * Vt) + (C * Vc) = (T + C) * Vm
Since the direction of the slide is northeast (45 degrees from north and east), we can break the sliding velocity into its components using trigonometry. The northeast direction can be split into equal north and east vectors.
Vm = Vx * cos(45°) + Vy * sin(45°)
To simplify the problem, we need to know the velocities or the angle between the vehicles before the collision. Unfortunately, the given information does not provide these details explicitly. Therefore, without further information, it is not possible to determine which vehicle was going faster before the collision.