Variable Mass and the Rocket Equation · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Throwing mass to gain speed

Science · Forces & Motion · ages 19-21
Name ______________________   Date ____________

  1. Which is the rocket equation for the speed gain?

    • Delta v equals exhaust speed times log of mass ratio
    • Delta v equals exhaust speed plus mass ratio
    • Delta v equals mass ratio over exhaust speed

  2. A rocket has no ground or air to push against. How does it move?

    • It throws mass backward and momentum pushes it forward
    • It pushes against the launch tower
    • It sails on the solar wind

  3. Two rockets share the same exhaust speed and the same mass ratio, but one is ten times heavier. Which gains more speed?

    • The heavier one
    • The lighter one
    • Neither: only the ratio matters

  4. Why is the rocket equation called unforgiving?

    • A bit more speed wants a lot more fuel
    • Fuel adds speed in exact proportion
    • Small rockets cannot reach orbit

  5. Why does staging beat carrying one large tank?

    • It raises the exhaust speed
    • It stops you hauling dead weight around
    • It removes gravity

  6. To set up the momentum balance, which system do you pick?

    • The rocket body alone
    • The rocket plus the gas it is about to eject
    • The exhaust gas alone

  7. Doubling the fuel load doubles the speed gain of a rocket.

    Circle one:   True   False

  8. Sam says rockets push against air, so they cannot work in empty space. What is wrong?

    • Rockets do need air, only higher up
    • Nothing external is needed: ejected mass carries the momentum
    • Rockets push against starlight instead
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Throwing mass to gain speed W1-mt_4IugclcEVi-s1

  1. Delta v equals exhaust speed times log of mass ratio · Integration of the momentum balance gives the log form.
  2. It throws mass backward and momentum pushes it forward · Ejected gas carries momentum back, so the rocket gains it forward.
  3. Neither: only the ratio matters · Absolute tons cancel; the equation sees just the ratio.
  4. A bit more speed wants a lot more fuel · The log grows slowly, so the fuel ratio must grow fast.
  5. It stops you hauling dead weight around · Dropping empty tanks restarts the mass ratio in your favour.
  6. The rocket plus the gas it is about to eject · That boundary turns the engine forces internal so they cancel.
  7. False · Speed follows the log of the ratio, which grows far slower.
  8. Nothing external is needed: ejected mass carries the momentum · The rocket pushes on its own exhaust, which is always aboard.
Worksheet · LightMySky