A tourist walks through a park following five successive displacements in the order…

PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

A tourist walks through a park following five successive displacements in the order listed below:

\mathbf{D}_1 = 50\,\hat{i}\,\text{m}

\mathbf{D}_2 = -30\,\hat{i}+40\,\hat{j}\,\text{m}

\mathbf{D}_3 = -60\,\hat{j}\,\text{m}

\mathbf{D}_4 = x\,\hat{i}+y\,\hat{j}\,\text{m}

(unknown components),

\mathbf{D}_5 = 10\,\hat{i}+20\,\hat{j}\,\text{m}

. After completing all five displacements the tourist finds herself

20\,\text{m}

directly east of the starting point. (i) Determine the values of

x

and

y

for

\mathbf{D}_4

that satisfy the given final position. (ii) Calculate the magnitude and direction of

\mathbf{D}_4

, measuring the direction as an angle with the positive

x

–axis. (iii) Find the total distance actually walked by the tourist along the five displacements.