Relative velocity question from giancoli physics

In summary, the conversation discusses a question about finding the angle theta given a picture with corrections and two velocities (600 km/h and 100 km/h). The person attempted to use the Pythagorean theory but ended up using the sine law to solve for theta. They were unsure of their answer and wanted to know what they did wrong. Another person suggests using the sine rule to solve for theta.
  • #1
hamsterpower7
43
0

Homework Statement


I attached the picture on the bottom (correction on the picture 30 degrees ---> 35 degrees sorry about that)
Vpa: 600 km/h
Vag:100 km/h

and the question is to find the angle theta

Homework Equations


The Attempt at a Solution



So I tried using Pythagorean theory by setting x and y

[tex] (V_pa)^2 =y^2 + x^2 [/tex]

set [tex] y = x/ (tan 35) [/tex]

so then I solved x = 344.1458617 Km/h

and since [tex] Sin/theta = (V_ag + x)/V_pa [/tex]

[tex] /theta = 47.75271609 [/tex]

sorry for ignoring the scientific notation,
I am not used to it :(

um anyways my answer was wrong
because the "solution" chose to use the 'sine law'
and that gives the right answer but I wanted to know what I did wrong to get the wrong answermuch appreciated
 
Last edited:
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  • #2
hamsterpower7 said:

Homework Statement


I attached the picture on the bottom (correction on the picture 30 degrees ---> 35 degrees sorry about that)
Vpa: 600 km/h
Vag:100 km/h

and the question is to find the angle theta

Homework Equations





The Attempt at a Solution



So I tried using Pythagorean theory by setting x and y

[tex] (V_pa)^2 =y^2 + x^2 [/tex]

set [tex] y = x/ (tan 35) [/tex]

so then I solved x = 344.1458617 Km/h

and since [tex] Sin/theta = (V_ag + x)/V_pa [/tex]

[tex] /theta = 47.75271609 [/tex]

sorry for ignoring the scientific notation,
I am not used to it :(

um anyways my answer was wrong
because the "solution" chose to use the 'sine law'
and that gives the right answer but I wanted to know what I did wrong to get the wrong answer


much appreciated

Your diagram shows right angled triangles. The real situation may not be right angled, which would necessitate use of sin rule or cos rule
 
  • #3
Okay I will post the question up to see if it wasn't a right angle

An airplane, whose air speed is 600km/h, is supposed to fly in a straight path 35 degrees north of east
but a steady 100km/h wind is blowing from the north
in what direction shuold the plane head?
 
  • #4
hamsterpower7 said:

Homework Statement


I attached the picture on the bottom (correction on the picture 30 degrees ---> 35 degrees sorry about that)
Vpa: 600 km/h
Vag:100 km/h

and the question is to find the angle theta

Homework Equations





The Attempt at a Solution



So I tried using Pythagorean theory by setting x and y

[tex] (V_pa)^2 =y^2 + x^2 [/tex]

set [tex] y = x/ (tan 35) [/tex]

so then I solved x = 344.1458617 Km/h

and since [tex] Sin/theta = (V_ag + x)/V_pa [/tex]

[tex] /theta = 47.75271609 [/tex]

sorry for ignoring the scientific notation,
I am not used to it :(

um anyways my answer was wrong
because the "solution" chose to use the 'sine law'
and that gives the right answer but I wanted to know what I did wrong to get the wrong answer


much appreciated

[Responding to your original so I can copy your symbols]

Your first line was incorrect

[tex] (V_pa)^2 =y^2 + x^2 [/tex]

It should read

[tex] (V_pg)^2 =y^2 + x^2 [/tex]

and since you don't know [tex] (V_pg)[/tex] it doesn't get you anywhere.

You have to use the sine rule on the triangle including theta to solve
 
  • #5
I would first commend you for attempting to use the Pythagorean theorem to solve this problem. However, it seems that you may have made a mistake in your calculations. Firstly, the value of x that you solved for (344.1458617 km/h) does not match the given value of V_ag (100 km/h). This indicates that there may have been an error in your calculation for x.

Additionally, the equation you used to solve for theta (Sin/theta = (V_ag + x)/V_pa) is incorrect. The correct equation should be sin(theta) = (V_ag + x)/V_pa. This may also have contributed to your incorrect answer.

I would recommend reviewing your calculations and equations to see if you can identify where you may have made a mistake. It is also important to pay attention to units when solving problems in physics, as they can greatly affect the final answer.

In terms of the "solution" using the sine law, this is a valid approach and may have given the correct answer. It is always good to explore different methods and approaches to problem-solving in physics. However, it is important to understand the reasoning behind each method and why it works, rather than just blindly following a solution. This will help you develop a deeper understanding of the concepts and improve your problem-solving skills. Keep up the good work in your studies!
 

1. What is relative velocity?

Relative velocity refers to the velocity of an object in relation to another object. It takes into account the motion of both objects and their respective velocities.

2. How is relative velocity calculated?

Relative velocity can be calculated by taking the difference between the velocities of the two objects and considering the direction of motion. If the objects are moving in the same direction, the relative velocity is the difference between their velocities. If they are moving in opposite directions, the relative velocity is the sum of their velocities.

3. What is the difference between relative velocity and absolute velocity?

Absolute velocity is the velocity of an object in relation to a fixed point or reference frame. Relative velocity, on the other hand, is the velocity of an object in relation to another moving object. Absolute velocity is constant, while relative velocity can change as the position and motion of the objects change.

4. How does relative velocity affect collisions?

Relative velocity plays a crucial role in collisions. The relative velocity between two objects at the point of collision determines the magnitude and direction of the impact. It also affects the amount of energy transferred between the objects during the collision.

5. Can relative velocity be negative?

Yes, relative velocity can be negative. This occurs when the two objects are moving in opposite directions, and the relative velocity is the sum of their velocities in opposite directions. A negative relative velocity indicates that the objects are moving away from each other.

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