A trekker starts from a camp at the origin and follows three successive displacements:

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

Problem

A trekker starts from a camp at the origin

O

and follows three successive displacements: (i) Write

\mathbf{w}

explicitly in terms of

\hat\imath

and

\hat\jmath

for a general value of

\lambda

. (ii) Obtain the resultant displacement

\mathbf{R}=\mathbf{u}+\mathbf{v}+\mathbf{w}

in component form. (iii) Determine the value of

\lambda

for which the trekker’s net displacement

\mathbf{R}

is perpendicular to the initial displacement

\mathbf{u}

. Also find the magnitude of

\mathbf{R}

for this value of

\lambda