What Is the Speed of Trucks After a Perfectly Inelastic Collision?

[jake40208]

Homework Statement

Two trucks with same masses are moving toward each other along a straight line with speeds of 50 mi/hr and 60 mi/hr. What is the speed of the combined trucks after completely inelastic collision?

Homework Equations

P$$_{}1$$+P$$_{}2$$= (2M) V$$_{}f$$

The Attempt at a Solution

Given the trucks we can assign a random mass. To make it easy Mass = 1. So 60+50= 2V$$_{}f$$ Solve it and you get 55 mi/hr. Is this correct?

 

[zack_21]

Think of the trucks as two vectors going the opposite direction. One with a magnitude of 50 mph and one with a magnitude of 60 mph. Take the sum of these two vectors.

 

[tomcue]

I would provide a more detailed and thorough response to this question.

First, it is important to clarify the concept of a perfect inelastic collision. In this type of collision, the two objects stick together after the collision and move as one combined object. This means that the total momentum of the system is conserved, but the kinetic energy is not.

In this particular scenario, we have two trucks with equal masses and different initial velocities. To solve for the final velocity of the combined trucks after the collision, we can use the principle of conservation of momentum. This states that the total momentum of a system before a collision is equal to the total momentum after the collision.

To use this principle, we can assign a variable for the final velocity of the combined trucks, let's call it V_f. We can also assign a variable for the mass of the trucks, let's call it M. Then, using the equation P_1 + P_2 = (2M)V_f, where P_1 and P_2 are the initial momenta of the two trucks, we can solve for V_f.

Plugging in the values given in the problem, we get (60 mi/hr)(1 kg) + (50 mi/hr)(1 kg) = (2 kg)V_f. Solving for V_f, we get V_f = 55 mi/hr. Therefore, the speed of the combined trucks after the collision is 55 mi/hr.

It is important to note that this solution assumes a perfectly inelastic collision, meaning that the two trucks stick together after the collision. In real-world scenarios, there may be some energy loss due to friction or other factors, which would affect the final velocity of the combined trucks. However, for the purposes of this problem, we can assume a perfect inelastic collision.