A 25000 kg truck moving at 40 m/s on a road angled at 17° hits a 10000 kg van moving at 25 m/s on a road angled at 60° at an intersection between two the two roads. Since this is a two-dimensional perfectly inelastic collision, what is the final velocity of the wreck?
To find the final velocity of the wreck after the collision, we can use the principles of conservation of momentum and conservation of energy.
First, let's break down the initial velocities of the truck (mass = 25000 kg) and the van (mass = 10000 kg) into their horizontal and vertical components.
For the truck:
- Horizontal component: 40 m/s * cos(17°)
- Vertical component: 40 m/s * sin(17°)
For the van:
- Horizontal component: 25 m/s * cos(60°)
- Vertical component: 25 m/s * sin(60°)
Next, let's calculate the total momentum before the collision. Since the collision is perfectly inelastic, the two vehicles will stick together after the collision.
The total momentum before the collision is the sum of the individual momenta:
Total momentum before collision = (mass of the truck * horizontal component of the truck's velocity) + (mass of the van * horizontal component of the van's velocity)
Next, let's calculate the final momentum after the collision. Since the two vehicles stick together, their total mass will be the sum of the individual masses.
The total momentum after the collision is the mass of the combined wreckage * final velocity.
Using the principle of conservation of momentum:
Total momentum before collision = Total momentum after collision
Now, we can equate the two momentum expressions and solve for the final velocity of the wreckage:
(mass of the truck * horizontal component of the truck's velocity) + (mass of the van * horizontal component of the van's velocity)
= (mass of the truck + mass of the van) * final velocity
Plug in the values and solve for the final velocity of the wreckage.
Note: In this case, we are assuming that there is no external force acting on the system, reducing the effect of friction and air resistance. Also, we assume no vertical forces act on the wreckage (i.e., no vertical acceleration).