Total Displacement of Duck on Pond: 86.7 m

[justgroovin]

Homework Statement

In a total time of 2.0 min, a duck on a pond paddles 22 m [36 degrees N of E] and then paddles another 65 m [E 25 degrees S]
Determine the duck's
i) total distance travelled
ii) average speed
iii) total displacement
iv) average velocity

Homework Equations

ii) v= delta d/t
iii) C = sqrt Cx^2 + Cy^2
iv) still working on it...was focusing on iii) for quite a while

The Attempt at a Solution

i) d = 87 m
ii) v = .73 m/s
iii)Ax = 22 cos 36 = 17.8 Bx = 65 cos 25 = 58.9
Ay = 22 sin 36 = 12.9 By = 65 sin 25 =27.5

Cx = 17.8 + 58.9 = 76.7
Cy = 12.9 + 27.5 = 40.4
C = √(〖Cx〗^2+〖Cy〗^2 )
C = √(5882.89+1632.16)
C = 86.7
Therefore, the total displacement is 86.7 m
I'm hoping I'm at least on the right track...I'm starting an online physics course with absolutely no background. Thanks for any help!

 

[Andrew Mason]

The Attempt at a Solution

i) d = 87 m
ii) v = .73 m/s
iii)Ax = 22 cos 36 = 17.8 Bx = 65 cos 25 = 58.9
Ay = 22 sin 36 = 12.9 By = 65 sin 25 =27.5

Cx = 17.8 + 58.9 = 76.7
Cy = 12.9 + 27.5 = 40.4
C = √(〖Cx〗^2+〖Cy〗^2 )
C = √(5882.89+1632.16)
C = 86.7
Therefore, the total displacement is 86.7 m
I'm hoping I'm at least on the right track...I'm starting an online physics course with absolutely no background. Thanks for any help!

The first rule of vector math is to Draw a vector diagram. In this case, it is a vector diagram of the two displacements.

You seem to have the right idea but you are making an error in adding the displacements. The y component of the second trip is in the opposite direction to the first. In the first trip the duck goes north. In the second, south. You can see that your answer must be wrong because you have the duck's displacement almost equal to the distance - which would have to be almost a straight line.

AM

 

[justgroovin]

Thank you for your help ...sorry for the delayed response, I'm apparently quite good at avoiding my physics course LOL. I appreciste the feedback.
So I ended up with total displacement = 78.1 m after I gave Cy a negative value of -14.6
Thanks again!