First slide

Scalars and Vectors

Question

A sail boat sails 2 km due East, 5 km 37^o South of East and finally an unknown displacement. If the final displacement of the boat from the starting point is 6 km due East, determine the third displacement.

Moderate

A

3 km, North
B

4 km, South
C

5 km, East
D

3 km, West

Solution

Given resultant displacement is 6 km due east
Which may be expressed as $6 \hat{i} .$
Given displacements are
(i) 2 km due east or $2 \hat{i}$
(ii) 5 km 37^o south of east its components
$\begin{array}{l} along x -axis = 5 \cos 37^{\circ} = 5 \times \frac{4}{5} = 4 \hat{i} \\ along y -axis = 5 \sin 37^{\circ} = 5 \times \frac{3}{5} = - 3 \hat{j} \end{array}$
(iii) unknown displacement let it be $a \hat{i} + b \hat{j}$
$\begin{array}{l} ∴ 2 \hat{i} + 4 \hat{i} - 3 \hat{j} + a \hat{i} + b \hat{j} = 6 \hat{i} \\ ∴ 6 \hat{i} + a \hat{i} - 3 \hat{j} + b \hat{j} = 6 \hat{i} \end{array}$
comparing the two sides
a=0 and b=3
$∴ Unknown displacement = 3 \hat{j}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App