A small repair drone of mass drifts near a disabled satellite

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Kinematics · Kinematics

Problem

A small repair drone of mass

6.0\,\text{kg}

drifts near a disabled satellite. Two identical cold-gas thrusters mounted orthogonally on the drone can fire in the

+x

and

+y

directions, respectively. A sequence of computer-controlled pulses is executed while on-board sensors record data. Piecewise description of the net external force components on the drone (SI units): Interval I:

0\le t<1.5\,\text{s}

•

F_{x}=+9.0\,\text{N}

•

F_{y}=+12.0\,\text{N}

Interval II:

1.5\,\text{s}\le t<3.0\,\text{s}

•

F_{x}=0\,\text{N}

•

F_{y}=+12.0\,\text{N}

Interval III:

3.0\,\text{s}\le t<4.0\,\text{s}

•

F_{x}=-9.0\,\text{N}

(opposite the

+x

direction) •

F_{y}=0\,\text{N}

Interval IV:

t\ge 4.0\,\text{s}

•

F_{x}=0\,\text{N}

•

F_{y}=0\,\text{N}

t=0

the drone is momentarily at rest at the origin of an inertial coordinate system:

\mathbf r_{0}=0

and

\mathbf v_{0}=0

. Neglect gravitational and other external influences. (a) For each interval, calculate the drone’s acceleration components

a_{x}

and

a_{y}

. (b) Determine the drone’s velocity components immediately after the end of each interval (at

t=1.5\,\text{s}

t=3.0\,\text{s}

, and

t=4.0\,\text{s}

). (c) Compute the drone’s position vector at

t=4.0\,\text{s}

. (d) Describe the drone’s motion for

t>4.0\,\text{s}

, and explain how your answer illustrates Newton’s first law and the concept of dimensional independence. (e) Suppose an unexpected micro-meteorite strike at

t=5.0\,\text{s}

delivers an impulse purely in the

+y

direction. Without performing additional calculations, predict qualitatively how the

x

and

y

components of the drone’s velocity will be affected and justify your reasoning.

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