Question

In: Physics

A runner jogs for 150 m due west (displacement A) and then turns to a direction...

A runner jogs for 150 m due west (displacement A) and then turns to a direction 30.0 degrees east of south and jogs for another 100 m (displacement B). Showing all work and units, and putting boxes around your answers, calculate

(a) the total distance between her initial and final positions. (Answer: 132 m)

(b) the direction of her net displacement C as an angle θC south of west. (Answer: 41°)

I am not really sure how to start this. Could someone please help with a STEP BY STEP explanation? I know you need to find the x and y components of A and B and then square both of those and take the square root to find C, but how would I go about doing that?

Expert Solution

Given:

A runner jogs for 150 m due west (displacement A) and then turns to a direction 30.0 degrees east of south and jogs for another 100 m (displacement B). Showing all work and units, and putting boxes around your answers, calculate

(a) the total distance between her initial and final positions. (Answer: 132 m)

(b) the direction of her net displacement C as an angle θC south of west. (Answer: 41°)

I am not really sure how to start this. Could someone please help with a STEP BY STEP explanation? I know you need to find the x and y components of A and B and then square both of those and take the square root to find C, but how would I go about doing that?

It is standard to use the positive x direction for east with unit vector , and the positive y direction for north with unit vector . We can then write for the first displacement vector --- . The magnitude of is and its angle is east of south --- in normal math angles measured from the positive x axis that is measured clockwise --- that is because angles are measured positive for counter clockwise from the positive x axis . We can then write in component form :

.

(a) The total displacement vector is just the vector sum of and :

. The distance from the initial to final position is just the magnitude of :

(b) The standard math angle of with respect to the positive x axis is then :

--- that is about clockwise from the positive x axis . We can call the angle from the west direction ( or negative x direction ) south of west .

genius_generous answered 1 year ago

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