Question

a man walks 5.0m due east, and then 10.0m N30oE find his resultant displacement?

Answer 1

Answer on Question 51823, Physics, Mechanics | Kinematics | Dynamics

Question:

A man walks $5.0m$ due east and then $10mN30{}^{\circ}E$ . Find his resultant displacement?

Solution:

The displacement $\mathbf{R}$ is the resultant when the two individual displacements $\mathbf{A}$ and $\mathbf{B}$ are added. We can find the magnitude of the resultant displacement $\mathbf{R}$ from the law of cosines applied to the triangle:

$$\theta = 1 8 0 {}^ {\circ} - 3 0 {}^ {\circ} = 1 5 0 {}^ {\circ},$$ $$\begin{array}{l} R = \sqrt {A ^ {2} + B ^ {2} - 2 A B c o s \theta} = \sqrt {(5 m) ^ {2} + (1 0 m) ^ {2} - 2 \cdot 5 m \cdot 1 0 m \cdot c o s 1 5 0 {}^ {\circ}} = \\ = 1 4. 6 m. \\ \end{array}$$

Then, we can find the direction of the resultant displacement $\mathbf{R}$ from the law of sines:

$$\frac {\sin \beta}{B} = \frac {\sin \theta}{R},$$ $$\sin \beta = \frac {B}{R} \sin \theta = \frac {1 0 m}{1 4 . 6 m} \cdot \sin 1 5 0 {}^ {\circ} = 0. 3 4 2 5,$$ $$\beta = \arcsin (0. 3 4 2 5) = 2 0 {}^ {\circ}.$$

Answer:

The magnitude of the resultant displacement is $R = 14.6m$ , direction is $N20{}^{\circ}E$ .

http://www.AssignmentExpert.com/