Question

At 363 ft tall, the Saturn V rocket was the largest rocket ever sent into space. Stage 1 of the rocket, built by Boeing,

has a fuel capacity of approximately 2520 tons and burns for 168 seconds. Assume that, during burn, the amount of
Stage 1 fuel onboard (in tons) is given by f(t) = 2520 – 15t with time measured in seconds. Calculate the derivative of f(t),
giving the appropriate units. What is the physical interpretation of the derivative?

Answer 1

f'(t) = -15 tons/second

Explanation:

Using the power rule, the derivative of f(t) is ...

f'(t) = -15 . . . tons/second

f(t) is the fuel weight, so f'(t) is the rate at which fuel weight is changing. The rocket is using fuel at the rate of 15 tons per second.

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Comment on units

The units of the equation for f(t) are ...

f(t) = 2520 tons - (15 tons/second)(t seconds)

The derivative is the coefficient of (t seconds), so is (-15 tons/second).