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Question 4 (6 marks) Veronica, an avid treasure hunter, spends her weekends wa...

Mar 15, 2024

Question 4 (6 marks) Veronica, an avid treasure hunter, spends her weekends walking down Rosedale beach. She brings a metal detector to help her find hidden objects under the sand. In doing this, she also helps keep Rosedale beach clean of unwanted items. On a Saturday morning, hunting for treasure, Veronica travelled

15 \mathrm{~m}

\left[220^{\circ}\right]

and then continued

25 \mathrm{~m}\left[335^{\circ}\right]

. a) Sketch and label a vector diagram to represent this scenario. (Communication: 2 marks) ROSEDALE ROSEDALE b) Calculate Veronica's resultant displacement relative to her initial starting point using components. (Application: 5 marks)

Solution by Steps

step 1

To represent Veronica's movements as vectors, we first convert the polar coordinates (magnitude and direction) to rectangular coordinates (x and y components)

step 2

The x-component of the first vector is calculated using

15 \cos(220^\circ)

step 3

The y-component of the first vector is calculated using

15 \sin(220^\circ)

step 4

The x-component of the second vector is calculated using

25 \cos(335^\circ)

step 5

The y-component of the second vector is calculated using

25 \sin(335^\circ)

step 6

Add the x-components from step 2 and step 4 to find the total x-component of Veronica's displacement

step 7

Add the y-components from step 3 and step 5 to find the total y-component of Veronica's displacement

step 8

Calculate the magnitude of Veronica's resultant displacement using the Pythagorean theorem with the total x and y components

Answer

The resultant displacement is the square root of the sum of the squares of the total x and y components.

Key Concept

Vector Addition and Conversion from Polar to Rectangular Coordinates

Explanation

To find the resultant displacement, we first convert the given polar vectors into rectangular components, add the respective components, and then use the Pythagorean theorem to find the magnitude of the resultant vector.