Elastic Collision: Solving for Velocity After Impact

In summary, the problem involves a 70kg man ice skating north and colliding with a 30kg boy ice skating west. After the collision, they are observed to be moving together at a velocity of 2m/s in a direction 37 degrees north of west. Using conservation of momentum and breaking it down into x and y directions, the final velocity of the boy can be solved for.
  • #1
dbb2112
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Homework Statement




A 70kg man who is ice skating north collides with a 30kg boy who is ice skating west. Immediately after the collision, the man and boy are observed to be moving together with a velocity of 2m/s in a direction 37 degrees north of west. What was the magnitude of the boy's velocity before collision.

Homework Equations





The Attempt at a Solution


I do not really know where to start. Could someone please list equations that are needed for this problem.
 
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  • #2
i meant to title inelastic
 
  • #3
use conservation of momentum, you should have an equation for the y-axis (north/south) and an equation for the x-axis (east/west)
 
  • #4
I do not see how to use it when only the final velocity is given.
 
  • #5
ok I am not sure if this is right, but i made the equation m2v2cos=m1v1'cos+m2v2'cos
and found v2 to equal 2.13 would that be my final answer?
 
  • #6
usually good to break these down into momentum in x direction and y direction

[itex]
M_{man}V_{man} \hat{y} = M_{final}V_{yfinal} \hat{y}
[/itex]
[itex]
M_{boy}V_{boy} \hat{x}=M_{final}V_{xfinal} \hat{x}
[/itex]
[itex]
M_{final} = M_{boy} + M_{man}
[/itex]
[itex]
V_{yfinal} = \left( 2 \frac{m}{s} \right) cos(37^{\circ})
[/itex]
see if you can determine the other final V and solve, let me know if you have questions on notation and such
 
Last edited:
  • #7
Thanks I am good now
 
  • #8
xcellent,

"may entropy increase in a way that favors your sword"
-Logicaltime
 

1. What is an elastic collision?

An elastic collision is a type of collision in which both the total momentum and total kinetic energy of the system are conserved. This means that the objects involved bounce off each other without any loss of energy, and the total momentum before and after the collision remains the same.

2. How do you calculate the velocities of objects after an elastic collision?

To calculate the velocities of objects after an elastic collision, you can use the conservation of momentum and conservation of kinetic energy equations. These equations are:

Initial total momentum = Final total momentum

Initial total kinetic energy = Final total kinetic energy

Using these equations and the masses and velocities of the objects before and after the collision, you can solve for the velocities after the collision.

3. What is the difference between an elastic collision and an inelastic collision?

Unlike an elastic collision, an inelastic collision is a type of collision in which there is a loss of kinetic energy. In an inelastic collision, objects stick together after the collision and move with a common velocity. The total momentum is still conserved, but the total kinetic energy is not.

4. Can the velocity of an object after an elastic collision be greater than its initial velocity?

No, the velocity of an object after an elastic collision cannot be greater than its initial velocity. This is because the conservation of kinetic energy equation states that the initial kinetic energy must be equal to the final kinetic energy, and since kinetic energy is directly proportional to velocity, the final velocity cannot be greater than the initial velocity.

5. What factors can affect the velocities of objects after an elastic collision?

The velocities of objects after an elastic collision can be affected by the masses of the objects, the velocities of the objects before the collision, and the angle at which the objects collide. In addition, external factors such as friction and air resistance can also affect the velocities of objects after a collision.

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