A small spacecraft of mass is coasting through deep space with a velocity of directed…

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A small spacecraft of mass

40\,\text{kg}

is coasting through deep space with a velocity of

12\,\text{m\,s}^{-1}

directed along the positive

x

-axis. At

t=0\,\text{s}

the pilot fires a maneuvering thruster that exerts a constant

120\,\text{N}

force for

4.0\,\text{s}

. The force acts in a direction

60^{\circ}

above the

+x

-axis in the

xy

-plane. No other forces of significance act on the spacecraft during the burn. (a) Draw and label a free-body diagram for the spacecraft while the thruster is firing. (b) Determine the components of the spacecraft’s acceleration in the

x

and

y

directions while the thruster is firing. (c) Calculate the spacecraft’s velocity components

v_x

and

v_y

immediately after the

4.0\,\text{s}

burn. (d) Determine the magnitude and direction (angle above the

+x

-axis) of the spacecraft’s velocity immediately after the burn. (e) Describe how the velocity of the spacecraft will change, if at all, after the thruster shuts off. Justify your answer with reference to Newton’s first law.

Related theory

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