What is the displacement for the couple's hiking trip? Give your answer as an ordered pair, with magnitude first, followed by a comma, then followed by the direction. Give the direction in terms of an angle measured CCW from the Easterly direction.

displacement = ( 4.045 km , 72 degrees )

Explanation:

Given:

- The radius if the circular path r = 2.5 km

- Couple hikes 70 % of the circular track.

Find:

What is the displacement for the couple's hiking trip? Give the direction in terms of an angle measured CCW from the Easterly direction.

Solution:

- The start point of the journey is west and due south in a circular direction.

- First we will determine the 70 % of the circumference of the circular path traveled. Using the arc length S formula:

                                       S = 0.70* ( 2*pi*r) = 7/5 pi*r

- The arc length calculated above is the distance traveled. However, we are interested in the "displacement" which is the shortest distance from start point to 70% of the track.

- The total amount of angle swept between the two points in radians is:

                                        S = r*Q

                                        Q = S / r = 7/5*pi

- The remaining angle angle to complete the full circle:

                                        Q' = 2*p - Q = 2*p -7/5*pi

                                        Q' = 0.6*pi.

- The displacement between two points can be calculated using sine rule as follows:

                     sin(Q') / displacement = sin (0.2*pi) / r

                     displacement = r*sin(Q') / sin (0.2*pi)

                     displacement = 2.5*sin(0.6*pi) / sin (0.2*pi)

                    displacement = 4.045 km

- The position with respect to the East direction is:

                                        pi - Q' = pi - 0.6*pi = 0.4*pi

Convert into degrees:               0.4*pi * 180 /pi = 72 degrees

in simple terms, the principle states that the buoyancy force on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational acceleration, g. this is also known as upthrust.