Solving a Bus Direction Change Problem

[jackscholar]

Homework Statement

A bus traveling at 65km/h on a bearing of 190° changes direction to south-east and continues at the same speed. Find the change in velocity of the bus.

Homework Equations

The Attempt at a Solution

I'm fairly hopeless at drawing the diagrams for these questions so I calculated the x and y components for both before and after the change in direction and i got:
65cos190=-64.01
65sin190=-11.29
65cos135=-45.96
65sin135=45.96
then i substracted vector 1 from vector 2 and got:
x=-45.96+64.01
y=45.96+11.29 (double - is positive)
x=18.05
y=57.25
thus r is √(18.05^2+57.25^2)=60.018
and the change in direction is thus inverse tan(57.25/18.05)=72.5 degrees
Is it viable to get an accurate answer without a diagram? And am I correct?

 

[Simon Bridge]

It is viable to use components to get an answer, but the method intrduces problems that you need to take care of when you use it.

* You need to define your directions formally, in words, and be careful about them. i.e.
... what are the x and y directions here? If +y is due north, and bearing is taken clockwise from due north, then cos(bearing) would be the y component.

If you used a diagram, the diagram provides the definitions as well as a handy reality check.

* You have extra steps to keep track of, with the extra minus signs and rounding errors this implies, providing more opportunity to make mistakes. Mistakes that will be hard to see from just the numbers.


With a protractor, the diagram is easy to draw.
The two vectors are the same length, 190deg is 10deg E of S, and SE is 45deg E of S.
Take the initial vector, reverse it, and put it's tail on the head of the final vector (final minus initial). The resultant goes from tail to head, forming an isosceles triangle with an apex angle of 35deg. The direction of the change, therefore, is easily produced exactly (no rounding needed) off the diagram.

You should practice drawing vectors and using triangles.
The skill becomes more important as you go on.

 

[jackscholar]

How do I reverse a vector?

 

[Simon Bridge]

Swap the head and the tail over.