How Do You Calculate Displacement and Angle of a Truck's Journey?

In summary: The final displacement from the origin is 26.17 km. In summary, the delivery truck traveled a total of 10 km north, 18 km east, and 29 km south, resulting in a final displacement of 26.17 km from the origin. To find the angle relative to the east, the Pythagorean theorem was used to calculate the displacement, and then the direction was determined using the formula tanθ = y/x where x = 18 km and y = -19 km. However, the response in the online homework system indicated that both answers were incorrect. Further clarification and guidance from an expert is needed.
  • #1
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1. A delivery truck travels 10 km north, 18 km east, and 29 km south.

a) What is its final displacement in km from the origin.

b) What is the angle in degree of the final displacement relative to the east.

2. I used the pythagorean theorem to obtain the final displacement from the origin. Then using the displacement found obtained the angle using sign 90 degrees.

3. First I drew an x/y coordinate system. The origin was at 0. Drew a line going 10 km north, 18 km east and 29 km south which puts me 19 km below the origin line.

18^2+19^2=685
The square root of 685 was 26.17 which was the final displacement from the origin.

For the angle, I calculated 26.17sin90 degrees which equaled 26.17. According to the online homework system, both answers were wrong.

What did I do wrong? Please advise. I am completely lost in physics so far.
 
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  • #2
Your calculation of the direction is wrong. You have net x displacement and y displacement. Then tanθ = y/x will give you the direction.
 
  • #3
Hi rl.bhat,

Physics is completely foreign to me. Please elaborate. If I use tan(theta)=y/x, what do I plus in for y and x? Also, how can I find final displacement (in km) from the origin?
 
  • #4
In the given problem x = 18 km and y = - 19 km.
 

1. What is 2D kinematics?

2D kinematics is the study of motion in two dimensions, usually in a two-dimensional coordinate system. It involves analyzing the position, velocity, and acceleration of an object in both the x and y directions.

2. How do you calculate the displacement of an object in 2D kinematics?

To calculate the displacement in 2D kinematics, you can use the Pythagorean theorem. The displacement is the vector sum of the object's displacement in the x-direction and y-direction.

3. What is the difference between velocity and speed in 2D kinematics?

Velocity is a vector quantity that describes the rate of change of an object's displacement in both the x and y directions. Speed, on the other hand, is a scalar quantity that describes the rate of change of an object's position without considering direction.

4. How do you find the acceleration of an object in 2D kinematics?

The acceleration of an object in 2D kinematics can be found by calculating the slope of the velocity-time graph in both the x and y directions. It can also be calculated by taking the derivative of the velocity function with respect to time.

5. Can you apply the equations of 1D kinematics to 2D motion?

Yes, the equations of 1D kinematics can be applied to 2D motion as long as you separate the motion into its x and y components. This means that the equations for displacement, velocity, and acceleration in the x-direction will be different from those in the y-direction.

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