Is my logic right for the answer to this inelastic car collision question?

That is the correct answer. In summary, the two cars, one weighing 1000 kg and the other weighing 1200 kg, collide at an intersection with initial velocities of 20.0 m/s north and 22.0 m/s east. After the collision, the two cars lock together and have a final velocity of 15.1 m/s east of north (52.8 degrees north east). This is determined by finding the total momentum of the system and solving for the final velocity using the equation P = mv. The direction is found using the arctan function.
  • #1
Lori

Homework Statement


A 1000 kg car approaches an intersection traveling north at 20.0 m/s . A 1200 kg approaches this same intersection traveling east at 22.0 m/s. The two car collides and lock together. Ignoring any external forces , what is the velocity of the car immediately after the collision.

a)29.7 m/s, 47.7 degrees east of north
b)21.1, 47.7 west of south
c)15.1 m/s, 52.8 east of north
d) 21.1 m/s , 52.8 east of north
e) 21.1 m/s 47.7 east of north

Homework Equations


P = mv (momentum)
Mass 1 car = 1000
mass 2 car = 1200

The Attempt at a Solution


This is a inelastic collision so the velocity final would be the same for the two objects with mass 1 + mass 2
First thing i would do would be to find Py (momentum in y direction) and Px (in x direction). If i find the magnitude by squaring them and tying the sqrt, I would be magnitude of momentum total. Thus, if i solve for v in P = mv, where m is the total mass, i can get v. The Py and Px will also give me the direction right?

My work:
Py = 1000kg*20 = 20000
Px = 1200kg*22 m/s = 26400
P = 33120.37 = mv
33129.37 = (1000+1200kg)v
v = 15.1 m/s and the direction is east of north (north west)
 
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  • #2
Your work looks good to me.
Lori said:
v = 15.1 m/s and the direction is east of north (north west)
Were you able to get the specific angle in degrees?

I don't understand why you would say that "east of north" is the same as "north west".
 
  • #3
oops, i meant north east!, yes, i took the arctan and got 52.8 degrees
 
  • #4
Lori said:
oops, i meant north east!, yes, i took the arctan and got 52.8 degrees
Sounds good!
 

Related to Is my logic right for the answer to this inelastic car collision question?

1. What is an inelastic car collision?

An inelastic car collision is a type of collision where the two objects involved stick together after impact. This results in a loss of kinetic energy and the objects moving together as one mass.

2. How does the elasticity of the objects affect the collision?

The elasticity of the objects involved in a collision determines the amount of kinetic energy that is conserved during the collision. In an inelastic collision, the objects have low elasticity and therefore, more kinetic energy is lost.

3. What factors determine the outcome of an inelastic car collision?

The outcome of an inelastic car collision is determined by several factors including the mass and velocity of the objects, as well as the angle and direction of the collision. The elasticity of the objects also plays a role in the outcome.

4. How can I determine the velocity of the objects after an inelastic car collision?

To determine the velocity of the objects after an inelastic collision, you will need to use the law of conservation of momentum. This states that the total momentum of the objects before the collision is equal to the total momentum after the collision. You will also need to know the mass and velocity of the objects before the collision.

5. What are some real-life examples of inelastic car collisions?

Some real-life examples of inelastic car collisions include car accidents where the vehicles involved stick together after impact, or a baseball hitting a catcher's glove and stopping rather than bouncing back. Another example is when a person jumps on a trampoline and the trampoline and person move together as one mass.

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