# Direction of the runner's total displacement?

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 dont 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.

## Answers and Replies

Homework Helper
Gold Member
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.

MIA6
how to find 35m's two components? because 35 is perpendicular, so...?

Throckmorton
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.

MIA6
so you mean 35m's x- component is 35m, too? and its y-component is itself?

Throckmorton
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)