How Do You Calculate Final Velocities in 2D Collisions?

TL;DR

To calculate the final velocities after a 2D collision, apply the conservation of momentum in both the x and y directions. Use the equations of motion to compile simultaneous equations for the two objects involved. By solving these for the final velocities, you find that the 5kg ball ends up moving at approximately 5.196 m/s, and the 3kg ball at about 5 m/s.

Transcript

so let's say if we have a five kilogram ball and it's moving east with a speed of six meters per second it strikes a three kilogram ball that is initially at rest now after the collision the three kilogram ball is going to go in this direction at an angle of 60 degrees with respect to the horizontal and the 5 kilogram ball after the collision is go... Read More

Key Insights

• ❣️ Momentum is conserved in both the x and y directions in a two-dimensional collision problem.
• ❣️ The x component of velocity is calculated using vcos(theta) and the y component using vsin(theta).
• ❓ By solving simultaneous equations, the final velocities of both objects can be found.

Questions & Answers

Q: What is the initial velocity of the 5kg ball in the x direction?

The initial velocity of the 5kg ball in the x direction is 6m/s because it was moving east.

Q: What is the final velocity of the 5kg ball in the x direction?

The final velocity of the 5kg ball in the x direction is v1 primecos(-30) = 4.33v1 prime.

Q: What is the equation for momentum conservation in the x direction?

The equation for momentum conservation in the x direction is m1v1x + m2v2x = m1v1x prime + m2v2x prime.

Q: How can the final velocity of the 3kg ball be calculated?

By substituting the value of v1 prime into the equation, we can solve for v2 prime.

Summary & Key Takeaways

• A 5kg ball moving east with a speed of 6m/s collides with a stationary 3kg ball.

• After the collision, the 3kg ball moves at a 60-degree angle to the horizontal, and the 5kg ball moves 30 degrees below the x-axis.

• To calculate the final velocities, the conservation of momentum and the x and y components of velocity are used.