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Talja [164]
3 years ago
7

A hiker leaves her camp and walks 3.5 km in a direction of 55° south of west to the lake. after a short rest at the lake, she hi

kes 2.7 km in a direction of 16° east of south to the scenic overlook. what is the magnitude of the hiker’s resultant displacement? round your answer to the nearest tenth

Physics
2 answers:
3241004551 [841]3 years ago
8 0

Let's choose east as positive x-direction and south as positive y-direction. We can resolve the two displacement along these two axes:

- Displacement 1 (3.5 km, 55^{\circ} south of west

d_{1x}=-(3.5 km)( cos 55^{\circ})=-2.01 km

d_{1y}=(3.5 km)( sin 55^{\circ})=2.87 km

- Displacement 2 (2.7 km, 16^{\circ} east of south

d_{2x}=(2.7 km)( sin 16^{\circ})=0.74 km

d_{1y}=(2.7 km)( cos 16^{\circ})=2.60 km

So, the total components on the two directions are

d_x = -2.01 km+0.74 km=-1.27 km

d_y=2.87 km+2.60 km=5.47 km

And the magnitude of the hiker's resultant displacement is

d=\sqrt{(1.27 km)^2+(5.47 km)^2}=5.6 km

tensa zangetsu [6.8K]3 years ago
3 0

Answer:

1.3km

Explanation:

We need to get the total displacement of the x and y components.

taking north and east as positive:

d_{1x}=-3.5km*cos(55^o)=-2km\\d_{2x}=2.7km*sin(16^o)=0.74km\\d_x=0.74km-2km=-1.26km

d_{1y}=-3.5km*sin(55^o)=-2.9km\\d_{2y}=-2.7km*sin(16^o)=-2.6km\\d_y=-2.6km-2.9km=-5.5km

The magnitude of the displacement is given by:

d=\sqrt{(d_x)^2+(d_y)^2}\\d=\sqrt{(-1.26)^2+(-0.3)^2}=5.64km

We were told to round it to the nearest tenth, so we have to look at the hundredth place, because it is equal or less than 4, the tenth place remains the same and we drop the numbers to the right.

d=5.6km

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