Vectors/Trigonometry Notation Problem

[lando45]

Hey,

I have been set this question:

The instantaneous acceleration of a runner as she rounds the curve on a track is <-1.5 , 0.5> m/s2.What is the magnitude of the acceleration of the runner and what angle does this vector make with respect to the +x axis?

But I don't really understand what the question is asking for, and what the <-1.5 , 0.5> means...any help?

Thanks a lot

 

[Fermat]

I imagine that <-1.5 , 0.5> are the components of her acceleration. i.e. her accln in the x-direction is -1.5 m/s² and in the y-direction, it's 0.5 m/s²


Does that help ?

 

[quicknote]

for reaching out for clarification on this question. It seems like you are struggling with the notation used in this problem. Let's break it down step by step.

First, the notation used in this problem is called vector notation. It is used to represent both the magnitude and direction of a physical quantity, in this case, acceleration. The notation is written as <x, y>, where x represents the magnitude of acceleration in the x-direction and y represents the magnitude of acceleration in the y-direction.

In this problem, the notation is < -1.5, 0.5 > m/s2. This means that the acceleration of the runner in the x-direction is -1.5 m/s2 and in the y-direction is 0.5 m/s2. The negative sign indicates that the acceleration is in the opposite direction of the positive x-axis.

Now, to answer the question, we need to find the magnitude of the acceleration and the angle it makes with respect to the +x axis. To find the magnitude, we can use the Pythagorean theorem, which states that the magnitude of a vector <x, y> is equal to the square root of x^2 + y^2. In this case, the magnitude of acceleration is √((-1.5)^2 + (0.5)^2) = √(2.25 + 0.25) = √2.5 m/s2.

To find the angle, we can use trigonometry. The angle with respect to the +x axis is given by the inverse tangent of y/x. In this case, the angle is tan^-1(0.5/-1.5) = -18.43 degrees. Note that the negative sign indicates that the angle is in the opposite direction of the positive x-axis.

I hope this helps to clarify the notation and how to solve this problem. If you have any further questions, please don't hesitate to ask. Good luck!