Final answer:
To find the change in velocity (Δv), subtract the initial velocity vector from the final velocity vector by performing vector arithmetic involving component breakdowns and subtraction, and then calculate the resultant vector magnitude and direction.
Step-by-step explanation:
The problem asks for calculating the magnitude of the change in velocity (Δv) when a physics student changes their driving speed and direction from 10.0 m/s [W30N] to 30.0 m/s [E20S]. To find the value of v, -V, we have to subtract the initial velocity vector from the final velocity vector. This involves a bit of vector arithmetic, which includes breaking down each velocity into its north-south and east-west components, subtracting these values respectively, and then finding the resulting vector's magnitude and direction.
For the initial velocity, the north and west components are found using trigonometry. Similarly, for the final velocity, the south and east components are calculated. Once these steps are taken, the components are subtracted accordingly: east minus west for the x component, and south minus north for the y component. The total change in velocity is then found by adding these components vectorially (which usually involves finding the vector's magnitude through the Pythagorean theorem and determining the direction with inverse trigonometric functions).
The options given in the question (A to D) seem to be unrelated to the expected calculations, possibly because they may refer to a different question or are incorrect. Therefore, no selection amongst A to D will yield the correct answer without performing the appropriate vector subtraction and calculation.