# Relative velocity question from giancoli physics

## 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

## The Attempt at a Solution

So I tried using Pythagorean theory by setting x and y

$$(V_pa)^2 =y^2 + x^2$$

set $$y = x/ (tan 35)$$

so then I solved x = 344.1458617 Km/h

and since $$Sin/theta = (V_ag + x)/V_pa$$

$$/theta = 47.75271609$$

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

Last edited:

PeterO
Homework Helper

## 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

## The Attempt at a Solution

So I tried using Pythagorean theory by setting x and y

$$(V_pa)^2 =y^2 + x^2$$

set $$y = x/ (tan 35)$$

so then I solved x = 344.1458617 Km/h

and since $$Sin/theta = (V_ag + x)/V_pa$$

$$/theta = 47.75271609$$

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

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?

PeterO
Homework Helper

## 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

## The Attempt at a Solution

So I tried using Pythagorean theory by setting x and y

$$(V_pa)^2 =y^2 + x^2$$

set $$y = x/ (tan 35)$$

so then I solved x = 344.1458617 Km/h

and since $$Sin/theta = (V_ag + x)/V_pa$$

$$/theta = 47.75271609$$

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

$$(V_pa)^2 =y^2 + x^2$$

$$(V_pg)^2 =y^2 + x^2$$
and since you don't know $$(V_pg)$$ it doesn't get you anywhere.