Conservation of Momentum Physics Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

medium
A 60 kg60 \text{ kg} astronaut floating in space throws a 5 kg5 \text{ kg} tool at 8 m/s8 \text{ m/s}. What is the astronaut's recoil velocity?

Solution

  1. 1
    Initial total momentum is zero (both at rest).
  2. 2
    By conservation of momentum: 0=mava+mtvt  ⟹  va=−mtvtma=−5×8600 = m_a v_a + m_t v_t \implies v_a = -\frac{m_t v_t}{m_a} = -\frac{5 \times 8}{60}
  3. 3
    va=−0.67 m/sv_a = -0.67 \text{ m/s}

Answer

vastronaut≈0.67 m/s (opposite direction)v_{\text{astronaut}} \approx 0.67 \text{ m/s (opposite direction)}
Conservation of momentum applies in isolated systems. The astronaut recoils in the opposite direction to the thrown tool, with a smaller speed due to greater mass.

About Conservation of Momentum

In a closed system with no net external force, the total momentum of all objects remains constant before and after any interaction — momentum is.

Learn more about Conservation of Momentum →

More Conservation of Momentum Examples

Example 1 medium

A [formula] cart moving at [formula] collides with a stationary [formula] cart. They stick together.

Example 2 hard

A [formula] ball moving at [formula] right collides elastically with a [formula] ball at rest. What

Example 4 medium

A [formula] firework initially at rest explodes into a [formula] piece moving east at [formula] and

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