11.A car being driven North at 12ms rounds a corner so that it is now being driven West at 16ms. Calculate the change in velocity of the car.

18.An athlete was running due East 5 ms when a southwesterly wind blowing at 2ms changes both his speed and the direction in which he was running. Calculate the magnitude of his new velocity.

Thx in advance :)

11. If you had a sketch, you'd have seen the answer quite easily... Draw it, it will help for sure. Draw a line upwards for the 12 m/s North and another line directly after the first one, this time, towards the left to represent the West direction, which is the final or resultant velocity. The change in velocity will be given when you draw the line which will give that resultant velocity.

18. A drawing here would help too...

For these numbers, you can use scale diagrams to help you see the magnitude and direction of the velocities involved. When you get used to them, you'll be able to visualise the diagram and proceed to the calculations directly.

You have to find the velocities with the question mark.

There is something wrong with 18. Maybe this is one that the teacher doesn't understand and is looking for a vector solution as Unknown has shown. But, as the problem is stated, there isn't enough information to solve.

For an airplane traveling through the air with the problem being to calculate the effect of wind on its path, you can simply add the vectors -- not really a change in velocity problem though since the airplane is still interacting with the air mass the same way; the air mass moving simply changes the path over the ground.

With a body on the on the ground, be it a person or a vehicle, it's not quite so simple. The runner's primary propulsion generating his velocity results from his contact with the ground. In calm air, there is a small amount of air resistance which could be shown as a relatively small vector directly opposing his path. To calculate this you'd need to be given a coefficient of wind resistance for the runner's body or something similar. Given that the runner is traveling at 5 m/s, this vector has already been subtracted from whatever his velocity would have been in a vacuum. To solve this, you'd need to apply the wind resistance coefficient to the 2 m/s, and vectorially add that to the 5 m/s vector.

Another way to visualize this. Consider the athlete running at 5 m/s as stated. If he suddenly encountered a 10 m/s headwind would it cause him to travel backwards as he is trying to run forward? Clearly the answer is no.

Often for classroom solutions we ignore the effects of friction and other small forces to help present problems and problem solutions in understandable form for students new to concepts. In this case though, it is invalid since it leads to major misconceptions on how objects interact with the planet and the air around it.

You're right Zazonker... I had hard times trying to cope with such situations which not always reflect the actual cases. However, that is what is asked in such levels. Later, the friction, and other small related forces will surely be included. I, for my part have not even included these in my works yet.