# Direction of the runner's total displacement?

• MIA6
In summary, the football player runs for a total of 50m with a displacement of 35m north and 15m east of north at an angle of 25 degrees from his original direction. This can be described as a resultant vector from the starting point to the ending point or by using coordinates (0,35) and (15,35) on a coordinate system where north is the positive Y axis and east is the positive X axis.
MIA6

## Homework Statement

A football player runs directly down the field for 35m before turning to the right at an angle of 25 degrees from his original direction and running an additional 15m before getting tackled. What is the magnitude and direction of the runner's total displacement?

2. The attempt at a solution
I drew a picture was like supposed that the player runs to north 35m first, and then turn to right, but the question here is which two sides form this 25 degrees angle? the one is 35m as a base, then draw the angle or draw a line that is parallel to x-axis as base, and draw the angle? Because i am not so sure about the pic, so i don't know how to do it. BTW, usually in the question that asks you to tell the direction, it means the angle between the resultant and "what"? i don't know the other side? hope you can give me a hint, thank you.

He runs north for 35m, then turns slightly right heading 25 degrees east of north, for 15m. The resultant displacement is the vector drawn from the start to the end point.

how to find 35m's two components? because 35 is perpendicular, so...?

There are two ways to describe vectors.

One way is by explicitly giving a magnitude and direction. In your case, the first vector's magnitude is 35 m, and it's direction is 90 degrees.

The other way to describe it is by using the coordinate system. (When adding vectors this is the easier of the two to use). The coordinates of the first vector is (0,35). It starts at (0,0) and goes up the y-axis 35 meters without changing in the x direction. (0,35) is the answer to your question above.

so you mean 35m's x- component is 35m, too? and its y-component is itself?

First off, North,East,South,West work in a clockwise fashion. North is the positive Y axis, East is the positive X axis, South is the negative Y axis, West is the Negative X axis.

So when he goes 35m to the north, he goes 35m up the y direction.

That makes the components of the 35m 0 in the X direction and 35 in the positive Y direction so: (0,35)

## 1. What is the direction of a runner's total displacement?

The direction of a runner's total displacement is the direction in which the runner is moving, relative to their starting point. It can be described using cardinal directions (north, south, east, west) or angles (0-360 degrees).

## 2. How is the direction of a runner's total displacement calculated?

The direction of a runner's total displacement can be calculated by finding the angle between the runner's starting point and ending point, relative to a reference direction (usually east or north). This can be done using basic trigonometry or vector analysis.

## 3. Can the direction of a runner's total displacement change?

Yes, the direction of a runner's total displacement can change if the runner changes their direction of movement. It can also change if the runner's starting point or reference direction changes.

## 4. How does the direction of a runner's total displacement affect their overall distance traveled?

The direction of a runner's total displacement does not affect their overall distance traveled. The distance traveled is only determined by the magnitude of the displacement (the straight-line distance between the starting and ending points), not the direction.

## 5. Why is it important to consider the direction of a runner's total displacement?

The direction of a runner's total displacement is important because it gives us a better understanding of the runner's movement and can be used to calculate other important quantities, such as speed and velocity. It also helps us determine the most efficient route for the runner to reach their destination.

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