Question

he Rocket Club is planning to launch a pair of model rockets. To build the rocket, the club needs a rocket body paired with an engine. The table lists the mass of three possible rocket bodies and the force generated by three possible engines.


Based on Newton’s laws of motion, which combination of rocket bodies and engines will result in the acceleration of 40 m/s2 at the start of the launch?

Body 3 + Engine 1
Body 2 + Engine 2
Body 1 + Engine 2
Body 1 + Engine 1

Answer 1

I don’t have the table of body masses and engine forces you mentioned. Can you paste those numbers?

Meanwhile, here’s how to decide which pair gives 40 m/s²:

- If you are neglecting gravity (using F = ma directly), required engine force for a body of mass m is
F = m · a = m · 40.
Compute F/m for each engine–body pair; any pair with F/m = 40 gives the required acceleration.

- If the rocket is launched upward and gravity must be included, the net upward acceleration a is
a = (F_thrust − mg)/m = F_thrust/m − g.
Rearranged, the engine must produce
F_thrust = m · (a + g) = m · (40 + 9.8) ≈ m · 49.8.
So check which engine’s thrust is approximately m·49.8 for the given body.

Paste the table (masses and thrusts) and tell me whether to include gravity, and I’ll compute which combination gives 40 m/s².