How Do You Calculate Displacement in Vector Kinematics?

[Tiplerfan]

Homework Statement

In a total time of 2.0 min, a duck on a pond paddles 22m [36deg N of E] and then paddles another 65 m [E 25deg S].

Determine the duck's

i) total distance...I answered this.
ii) average speed...I answered this.
iii) total displacement...This is my dilema.
iv) average velocity...I can aswer this one once I know the displacement.

Homework Equations

I'm really not sure how to go about finding the displacement when angles are involved. Do I use trig or one of the formula's?

The Attempt at a Solution

Using trig on the vector diagram I came up with a displacement of 34m [E 25deg S].

 

[esalihm]

split the two displacements into componenets (N,W,S,E)
then sum them up (but don't forget to subtract when necessary)
I mean use vector sum :)

 

[m2003]

I can provide a response to this content by explaining the basic kinematics involved in the duck's paddle. Kinematics is the study of motion without considering its causes, and it is an important part of physics that helps us understand the movement of objects.

In this scenario, the duck's motion can be described in terms of its distance, displacement, speed, and velocity. Distance is the total length of the path traveled, while displacement is the shortest straight-line distance between the initial and final positions. Speed is the rate at which the duck covers distance, while velocity is the rate at which its displacement changes over time.

To determine the duck's total distance, we simply add the two given distances of 22m and 65m, giving us a total of 87m. Similarly, to calculate the average speed, we divide the total distance by the total time, which gives us a speed of 43.5m/min.

To find the total displacement, we need to consider both the magnitude (distance) and direction of the duck's motion. In this case, we can use the Pythagorean theorem to calculate the magnitude of the displacement, which is the square root of the sum of the squares of the two given distances. This gives us a displacement of 68.7m. To determine the direction of the displacement, we can use trigonometry to find the angle between the initial and final positions. This gives us a displacement of 68.7m [E 25deg S].

Finally, to calculate the average velocity, we divide the total displacement by the total time, which gives us a velocity of 34.35m/min [E 25deg S]. This tells us that the duck's average velocity is in the direction of its displacement, which is towards the east-southeast.

In conclusion, by understanding the basic kinematics involved in the duck's paddle, we can accurately describe and analyze its motion in terms of distance, displacement, speed, and velocity. This can be applied to any object's motion and helps us better understand the physical world around us.