Ice skaters collision with angle

In summary, the problem involves two ice skaters with different masses and velocities colliding with each other. After the collision, one skater's velocity changes to 4 m/s at an angle of 25 degrees relative to their original direction. To determine the velocity of the other skater after the collision, the equations for components of momentum are used, taking into account the magnitude and angle of the initial velocity. The final velocity is a vector with both magnitude and direction, which can be found using the arctan function.
  • #1
fantisism
16
0

Homework Statement


Two ice skaters crash into each other. Before they collide, one of them (50 kg) is skating in a straight line at 5 m/s, the other (40 kg) is skating at 4 m/s in a straight line at 90 degrees to the 50 kg skater’s direction. After the collision, the 50 kg skater is moving at 4 m/s at an angle of 25 degrees relative to their original direction. Calculate the velocity of the 40 kg skater after the collision. Is the total kinetic energy constant?

Homework Equations


m1v1ix+m2v2ix=m1v1fx+m2v2fx
m1v1iy+m2v2iy=m1v1fy+m2v2fy

The Attempt at a Solution


I drew a diagram before collision and after collision. Really, all I need to know is where in the formula(s) would I need to include the angle and I SHOULD be able to figure it out from there.
FullSizeRender.jpg
 
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  • #2
You have v1fx and v1fy in the equations for components of momentum. How do you get them, knowing magnitude and angle of velocity ?
 
  • #3
ehild said:
You have v1fx and v1fy in the equations for components of momentum. How do you get them, knowing magnitude and angle of velocity ?
Is v1fx=(4 m/s)(cos(25°)) and v1fy=(4 m/s)(sin(25°))?
 
  • #4
fantisism said:
Is v1fx=(4 m/s)(cos(25°)) and v1fy=(4 m/s)(sin(25°))?
Yes.
 
  • #5
ehild said:
Yes.
And then with that information, solve for v2fx and v2fy?
 
  • #6
fantisism said:
And then with that information, solve for v2fx and v2fy?
Yes.
 
  • #7
ehild said:
Yes.
And then once I figure out what those two velocities are, I would square them individually and take the square root of the sums? So, sqrt((v2fx)2+(v2fy)2? And that would be the answer for the first question?
 
  • #8
fantisism said:
And then once I figure out what those two velocities are, I would square them individually and take the square root of the sums? So, sqrt((v2fx)2+(v2fy)2? And that would be the answer for the first question?
The final velocity is asked. It is a vector with magnitude and direction. I think the problem wants both the magnitude and angle.
 
  • #9
ehild said:
The final velocity is asked. It is a vector with magnitude and direction. I think the problem wants both the magnitude and angle.
To find the angle, would it be arctan(v2fy/v2fx)?
 
  • #10
fantisism said:
To find the angle, would it be arctan(v2fy/v2fx)?
Yes.
 
  • #11
Alright. I can solve the second subquestion myself. Thank you again!
 

FAQ: Ice skaters collision with angle

1. How does the angle of collision affect the outcome of ice skaters colliding?

The angle of collision between two ice skaters can greatly impact the force and direction of their collision. If the angle is perpendicular, the skaters will collide head on and experience the most force. However, if the angle is more oblique, the force will be distributed differently and the direction of movement after the collision may change.

2. What physical factors contribute to the outcome of a collision between ice skaters?

The mass, velocity, and momentum of each skater are the main physical factors that contribute to the outcome of a collision. The greater the mass and velocity, the more force will be exerted during the collision. Momentum, which is mass multiplied by velocity, also plays a role in determining the direction of movement after the collision.

3. How do the laws of physics apply to ice skaters colliding at an angle?

The laws of physics, specifically Newton's laws of motion, apply to ice skaters colliding at an angle. The first law, also known as the law of inertia, states that an object will remain at rest or in motion unless acted upon by an external force. The second law, which relates force, mass, and acceleration, explains how the angle and mass of the skaters will affect the force of the collision. The third law, or the law of action and reaction, explains how for every action there is an equal and opposite reaction, which is evident in the direction of movement after a collision.

4. How do different angles of collision affect the potential for injury in ice skaters?

The angle of collision can greatly impact the potential for injury in ice skaters. A head-on collision at a perpendicular angle has the highest potential for injury due to the force and direction of movement. However, collisions at more oblique angles may distribute the force differently and result in less severe injuries. The angle of collision also affects the potential for injury to specific body parts, such as the head or legs.

5. How can ice skaters minimize the risk of injury in collisions with angles?

To minimize the risk of injury in collisions with angles, ice skaters can focus on maintaining proper form and technique while skating. This includes keeping their center of mass over their skates, using their arms and legs to absorb impact, and being aware of their surroundings to avoid collisions. Wearing appropriate safety gear, such as helmets and padding, can also help reduce the risk of injury in case of a collision.

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