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A bicyclist travels 4.5 km west, then travels 6.7 km at an angle 27.0 degrees South of West. What is the magnitude of the bicyclist's total displacement?

Sagot :

abidemiokin

Answer:

10.90km

Explanation:

Magnitude of the total displacement is expressed using the equation

d = √dx²+dy²

dx is the horizontal component of the displacement

dy is the vertical component of the displacement

dy = -6.7sin27°

dy = -6.7(0.4539)

dy = -3.042

For the  horizontal component of the displacement

dx = -4.5 - 6.7cos27

dx = -4.5 -5.9697

dx = -10.4697

Get the magnitude of the bicyclist's total displacement

Recall that: d = √dx²+dy²

d = √(-3.042)²+(-10.4697)²

d = √9.2538+109.6146

d = √118.8684

d = 10.90km

Hence the magnitude of the bicyclist's total displacement is 10.90km

The bicyclist magnitude of displacement is equal to 9.62m

Resolution of Vectors

To find the resultant magnitude of the bicyclist total displacement, we have to find the x and y component.

For the first direction, the components are

[tex]x_1 = -4.5i[/tex]

sine we don't have any vertical displacement, the y-component is equal to zero.

for the second direction,

[tex]x_2 = -6.7sin27i\\y_2= 6.7cos27j[/tex]

The resultant x and y component are;

  • [tex]R_x = -4.5i + (-6.7sin27i)\\R_x = -7.54i[/tex]
  • [tex]R_y = 0 + 6.7cos27= 5.97j[/tex]

Let's find the magnitude of displacement

[tex]R = \sqrt{R_x^2 + R_x^2}\\R = \sqrt{(-7.54)^2 + (5.97)^2 }\\\\R = 9.62m[/tex]

The bicyclist magnitude of displacement is equal to 9.62m

Learn more on resolution of vectors here;

https://brainly.in/question/3543542

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