Question

A truck travels 1430 m uphill along a road that makes a constant angle of 5.76◦ with the horizontal. Find the magnitude of the truck's horizon- tal component of displacement. Answer in units of m.

Answer 1

1422.8 m

Step-by-step explanation:

Given:

Displacement of the truck is,
`\vec S=1430\ m`

The direction of the truck's displacement is 5.76° with the horizontal.

A vector inclined at angle
`\theta` with the horizontal is resolved into 2 components which are mutually perpendicular to each other. One of the component is along the horizontal and the other is along the vertical.

If a vector 'A' is inclined at an angle
`\theta` with the horizontal, then its horizontal and vertical components are given as:

`Horizontal:\\A_x=A\cos \theta\\\\Vertical:\\A_y=A\cos \theta`

Here, the vector is 'S' and its horizontal component is needed.

Therefore, the horizontal component is given as:

`S_x=S\cos \theta\\S_x=1430* \cos(5.76\°)\\S_x=1422.8\ m`