A cyclist moves 100m north,75m east, and 60m South. Calculate resultant displacement?

To calculate the resultant displacement, we need to use the Pythagorean theorem to find the magnitude of the displacement and the tangent function to find the direction of the displacement.

The magnitude of the displacement is:

```
|d| = √(dx^2 + dy^2)
```

where dx is the displacement in the x-direction and dy is the displacement in the y-direction.

In this case, dx = 75m and dy = 100m - 60m = 40m. Therefore, the magnitude of the displacement is:

```
|d| = √(75^2 + 40^2) = 85m
```

The direction of the displacement is given by the angle θ, where:

```
θ = tan^-1(dy/dx)
```

In this case, θ = tan^-1(40/75) = 29.7°.

Therefore, the resultant displacement is 85m at an angle of 29.7° north of east.