A drone starts from the origin (O(0,0) ) and finally reaches the point (P(15

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

Problem

A drone starts from the origin

O(0,0)

and finally reaches the point

P(15\,\text{m},\,20\,\text{m})

in two consecutive straight-line flights. During the first flight it travels

12\,\text{m}

at an angle of

40^{\circ}

above the positive

x

-axis. Let

\mathbf{d}_1

and

\mathbf{d}_2

be the displacement vectors for the first and second flights respectively. (i) Resolve

\mathbf{d}_1

into its rectangular components. (ii) Write the vector equation connecting

\mathbf{d}_1, \mathbf{d}_2

and the overall displacement

\overrightarrow{OP}.

(iii) Determine the components of

\mathbf{d}_2.

(iv) Calculate the magnitude of

\mathbf{d}_2

and the direction it makes with the positive

x

-axis. (v) Comment on whether the two displacement vectors form the two adjacent sides of a triangle whose third side is

\overrightarrow{OP}.

Justify your answer with vector addition.