A rocket’s thrust force at time seconds is given by

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

A rocket’s thrust force at time

t

seconds is given by

F(t)=m(t)v(t)

, where

m(t)

is the rocket’s mass in kilograms and

v(t)

is its exhaust velocity in meters per second. At

t=4\text{ s}

, the following data are recorded:

m=50\text{ kg}

\dfrac{dm}{dt}=-0.2\text{ kg/s}

v=30\text{ m/s}

, and

\dfrac{dv}{dt}=5\text{ m/s}^2

. Determine

\dfrac{dF}{dt}

, the instantaneous rate of change of thrust at this instant. (a)

250\ \text{N/s}

(b)

256\ \text{N/s}

(c)

244\ \text{N/s}

(d)

140\ \text{N/s}