A 1000kg compact car is travelling north at 15m/s when it collides with a truck travelling east at 10m/s. All occupants are wearing seat belts and there are no injuries, but the two vehicles are thoroughly tangled and move away from the impact point as one mass. The insurance adjustor has asked you to find the velocity of the wreckage just after the impact. What do you tell her?
momentum is conserved ... but you need the mass of the truck to give an exact answer
useful
To find the velocity of the wreckage just after the impact, we can use the principles of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.
First, let's find the momentum of the car and the truck before the collision. The momentum is calculated by multiplying the mass of an object by its velocity.
Momentum of the car = mass of the car × velocity of the car
= 1000 kg × 15 m/s
= 15000 kg·m/s
Momentum of the truck = mass of the truck × velocity of the truck
= unknown (let's call it m) × 10 m/s
= 10m kg·m/s
So, the total momentum before the collision is 15000 kg·m/s + 10m kg·m/s.
Next, we need to find the momentum of the wreckage just after the impact. Since the car and the truck move away from the impact point as one mass, their masses can be combined. Let's call the mass of the wreckage M'.
The total momentum after the collision is M' × velocity of the wreckage.
According to the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Therefore:
15000 kg·m/s + 10m kg·m/s = M' × velocity of the wreckage
We have one equation with two unknowns (M' and velocity of the wreckage). To solve for the velocity of the wreckage, we need another equation or more information, such as the mass of the truck or the mass of the wreckage.
Without more information, we cannot determine the velocity of the wreckage just after the impact. Therefore, we need additional data to provide a specific answer to the insurance adjustor.