(Components with mixed units and bearing notation) An aircraft is reported to fly at…

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

Problem

(Components with mixed units and bearing notation) An aircraft is reported to fly at

550\,\text{km}\,\text{h}^{-1}

on a bearing of

042^{\circ}\,30'

. Treat east as the

+x

-axis and north as the

+y

-axis. (i) Convert the stated speed into

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

, giving your answer to three significant figures. (ii) Resolve the horizontal velocity into its

x

and

y

components in

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

. (iii) During a climb the aircraft maintains these horizontal components while gaining

1200\,\text{m}

of altitude in

90\,\text{s}

. Taking upward to be the

+z

-direction, determine the unit vector that points along the resultant three-dimensional velocity vector at the end of the

90\,\text{s}

interval.