(Figure 1) shows a map of Olivia\'s trip to a coffee shop. She gets on her bike

Question

(Figure 1) shows a map of Olivia's trip to a coffee shop. She gets on her bike at Loomis and then rides south 0.7mi to Broadway. She turns east onto Broadway, rides 0.8 mi to where Broadway turns, and then continues another 1.2mi to the shop.

Part A

Part complete

What is the magnitude of the total displacement of her trip?

Express your answer in miles.

1.8

Correct

Part B

What is the direction of the total displacement of her trip?

Express your answer in degrees.

???????   

1 of 1

(Figure 1) shows a map of Olivia's trip to a coffee shop. She gets on her bike at Loomis and then rides south 0.7mi to Broadway. She turns east onto Broadway, rides 0.8 mi to where Broadway turns, and then continues another 1.2mi to the shop.

Part A

Part complete

What is the magnitude of the total displacement of her trip?

Express your answer in miles.

d =

1.8

  mi

Correct

Part B

What is the direction of the total displacement of her trip?

Express your answer in degrees.

=

???????   

  , measured counterclockwise
from the eastward direction Figure

1 of 1

Start End Broad130

Explanation / Answer

Given,

Starting point: x = 0, y = 0.7

Intersection is at x = 0, y = 0

Broadway bends at x = 0.8, y = 0.

End is at x = [0.8 + (cos 30 x 1.2)] = 1.84

and y = (sin 30 x 1.2) = 0.6

Total displacement is from 0, 0.7 to 1.84, 0.6

dx is 1.84 and dy is -0.1

Displacement D = sqrt(1.84^2 + 0.1^2) = 1.843 mi

b)

Direction, theta = [90 + (arctan 0.1/1.84)] or 93.11 degrees clockwise from true north.

Comment in case any doubt, please rate my answer....

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