Self-Assessment Quiz: The Rocket Equation

Twenty questions to check your grasp of the rocket equation, specific impulse, staging, and delta-v budgets. Answer each before opening the key. Aim for 16 or more. Use $g_0 = 9.81\ \text{m/s}^2$.

Question 1

In $\Delta v = v_e \ln(m_0/m_f)$, the quantity $m_0/m_f$ is called the:

A) propellant fraction B) mass ratio C) specific impulse D) thrust-to-weight ratio

Question 2

The rocket equation is derived from:

A) conservation of energy B) Newton's law of gravitation C) conservation of momentum D) the ideal gas law

Question 3

Doubling the target delta-v (at fixed $v_e$) changes the required mass ratio by:

A) doubling it B) squaring it C) adding a constant D) halving it

Question 4

Specific impulse $I_{sp}$ and exhaust velocity $v_e$ are related by:

A) $I_{sp} = v_e / g_0$ B) $I_{sp} = v_e \cdot g_0$ C) $I_{sp} = v_e^2$ D) they are unrelated

Question 5

Roughly what fraction of an orbital rocket's lift-off mass is propellant?

A) ~25% B) ~50% C) ~90% D) ~99.9%

Question 6

The main reason staging increases achievable delta-v is that it:

A) adds more propellant B) increases the exhaust velocity C) stops accelerating empty structure once it's no longer needed D) reduces gravity losses

Question 7

A stage with $v_e = 3{,}000\ \text{m/s}$ and mass ratio $e$ (≈ 2.718) delivers a delta-v of:

A) $3{,}000\ \text{m/s}$ B) $1{,}000\ \text{m/s}$ C) $8{,}150\ \text{m/s}$ D) $2{,}718\ \text{m/s}$

Question 8

"Delta-v is the currency of spaceflight" means:

A) delta-v is measured in dollars B) every maneuver has a delta-v cost and a rocket carries a fixed delta-v budget C) thrust determines how far you can go D) delta-v equals the fuel mass

Question 9

Which propellant combination has the highest specific impulse?

A) solid propellant B) LOX / RP-1 (kerosene) C) LOX / liquid hydrogen D) cold gas

Question 10

An engine with $I_{sp} = 450\ \text{s}$ has an exhaust velocity of about:

A) $450\ \text{m/s}$ B) $4{,}400\ \text{m/s}$ C) $45\ \text{m/s}$ D) $9{,}810\ \text{m/s}$

Question 11

Which quantity does not appear in the rocket equation?

A) exhaust velocity B) initial mass C) thrust D) final mass

Question 12

Electric propulsion has very high $I_{sp}$ but is unsuitable for launch because it has:

A) low exhaust velocity B) extremely low thrust C) no propellant D) negative delta-v

Question 13

Making a rocket geometrically ten times larger, keeping proportions the same, changes its delta-v by:

A) ×10 B) ×100 C) no change D) ÷10

Question 14

The delta-v map shows that, from Earth's surface, the single most expensive leg (in delta-v) is:

A) LEO → GEO B) surface → LEO C) LEO → Mars transfer D) low lunar orbit → Moon surface

Question 15 (True/False, justify)

"A rocket with more thrust always reaches a higher delta-v." True or false? Justify in one sentence.

Question 16 (True/False, justify)

"Because $v_e$ sits in the exponent of the mass ratio, a 10% improvement in exhaust velocity is worth more than a 10% improvement in mass ratio." True or false? Explain briefly.

Question 17 (True/False, justify)

"Two stages that each deliver 4 km/s give a combined 8 km/s." True or false? Say why.

Question 18 (Short answer)

Explain in one or two sentences why the propellant fraction needed for orbit (~94%) leaves so little room for payload, and how staging helps.

Question 19 (Short answer)

A stage has $m_0 = 400\ \text{t}$, $m_f = 100\ \text{t}$, $v_e = 3{,}000\ \text{m/s}$. Compute its delta-v (show the mass ratio and the logarithm).

Question 20 (Short answer)

In your own words, what is "the tyranny of the rocket equation," and name one engineering response to it that appears in this chapter.

Answer Key

Topics to review by question