Question

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?

Answer 1

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

Answer 2

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

$x_1 = -4.5i$

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

for the second direction,

$x_2 = -6.7sin27i\\y_2= 6.7cos27j$

The resultant x and y component are;

• $R_x = -4.5i + (-6.7sin27i)\\R_x = -7.54i$
• $R_y = 0 + 6.7cos27= 5.97j$

Let's find the magnitude of displacement

$R = \sqrt{R_x^2 + R_x^2}\\R = \sqrt{(-7.54)^2 + (5.97)^2 }\\\\R = 9.62m$

The bicyclist magnitude of displacement is equal to 9.62m

Learn more on resolution of vectors here;

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