Chapter 3: Q3E (page 121)

Find the north and east components of the displacement for the hikers shown in Figure.

Short Answer

Expert verified

The east component is 3.8 km

The north component is 3.2 km

Step by step solution

Vector definition

A vector is a quantity that has both magnitude and direction. Displacement, velocity, force, torque, and other vector quantities are some examples of vector quantities.

Determine the displacement of the hiker towards the north component

In triangle ABC:

$\begin{array}{rcl} ∠ A B C & = & 90^{°} - 40^{°} \\ = & 50^{°} \end{array}$

$BC = 5 km$

AC = Base

BC = Hypotenuse

AB = Perpendicular

For the north component, in the right-angled triangle:

$\begin{array}{rcl} \cos θ & = & \frac{b a s e}{h y p o t e n o u s} \\ \cos 50^{°} & = & \frac{b a s e}{5} \\ 0.64 & = & \frac{b a s e}{5} \\ b a s e & = & 3.2 k m \end{array}$

Therefore, towards the north component, the displacement of the hiker is 3.2 km.

Step 3: Determine the displacement of the hiker towards the east component

For the east component, in a right-angled triangle:

$\begin{array}{rcl} \sin θ & = & \frac{P e r p e n d i c u l a r}{h y p o t e n o u s} \\ \sin 50^{°} & = & \frac{p e r p e n d i c u l a r}{5} \\ 0.77 & = & \frac{p e r p e n d i c u l a r}{5} \\ P e r p e n d i c u l a r & = & 0.77 \times 5 \\ p e r p e n d i c u l a r & = & 3.8 k m \end{array}$

Therefore, towards the east component, the displacement of the hiker is 3.8 km.

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Find the north and east components of the displacement for the hikers shown in Figure.

Short Answer

Step by step solution

Vector definition

Determine the displacement of the hiker towards the north component

Step 3: Determine the displacement of the hiker towards the east component

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