2-dimensional momentum problem | Impacts and linear momentum | Physics | Khan Academy

TL;DR

A ball A with a mass of 10kg and velocity of 3m/s collides with ball B, and after the collision, ball A moves in a new trajectory. The problem is to determine the velocity of ball B.

Transcript

Welcome back. We will now do a momentum problem in two dimensions. So let's see what we have here. So we have this ball A and we could maybe even think of it as maybe what's going on on the surface of a pool table. We have ball A and it's moving with its 10 kilograms. So these numbers are the mass of the balls. This is a 10 kilogram ball and it's m... Read More

Key Insights

• 💥 Momentum is conserved in both magnitude and direction in a collision.
• ❣️ Breaking down momentum into x and y components helps solve problems in multiple dimensions.
• ❣️ The x and y components of velocity can be found using trigonometry.

Questions & Answers

Q: How do you determine the momentum in each direction in a two-dimensional collision?

In a two-dimensional collision, you break down the momentum into the x and y components. The initial momentum in each direction must be equal to the final momentum in each direction.

Q: What is the initial momentum of ball B in the x direction?

Since ball B has no initial velocity in the x direction, its momentum in the x direction is zero.

Q: How do you find the x and y components of ball A's velocity?

To find the x component, use the cosine of the angle between the x-axis and the velocity vector. To find the y component, use the sine of the angle.

Q: What is the velocity of ball B in the y direction after the collision?

The momentum of ball B in the y direction is 10 kg m/s. Dividing this by its mass of 5kg gives a velocity of 2 m/s.

Summary & Key Takeaways

• Ball A with a mass of 10kg and velocity of 3m/s collides with ball B, which has a mass of 5kg.

• After the collision, ball A moves at a 30-degree angle with a velocity of 2m/s.

• The problem is to determine the velocity of ball B after the collision.