(b) collisions and interaction of bodies in one dimension and in two…

The idea

Momentum conservation applies along each perpendicular direction independently. In one dimension, choose a positive axis and solve m_A u_A + m_B u_B = m_A v_A + m_B v_B. In two dimensions, resolve all velocities into x and y components, then conserve momentum separately in each direction: total p_x before equals total p_x after, and total p_y before equals total p_y after. For example, a ball moving east at 4.0 m s⁻¹ striking a stationary ball and deflecting at 30° requires x and y equations to find both final velocities. Draw a vector diagram, resolve with sine and cosine, and solve the simultaneous equations.

What earns the marks

• Momentum is conserved independently in each perpendicular direction for a system with no resultant external force.
• In one dimension, velocities are given signs along a single chosen axis.
• In two dimensions, resolve velocities into components and write separate conservation equations for x and y.
• Vector diagrams or component tables help track before and after momenta in two dimensions.

Common mistakes and how to put them right

• Conserving momentum only along the original direction of motion in a two-dimensional collision.

  Put it right: The correct method conserves momentum along both perpendicular axes.

• Mixing up sine and cosine when resolving a velocity at an angle.

  Put it right: The correct component adjacent to the angle uses cosine and the perpendicular component uses sine.

• Adding component magnitudes without signs.

  Put it right: The correct approach assigns positive and negative directions on each axis.

Exam tips

• Draw a clear before-and-after diagram with axes labelled and angles marked.
• Make a component table for x and y momenta before and after the collision.
• Solve the simpler axis equation first, then substitute into the other to find the remaining unknown.