Question

A truck travels 1450 m uphill along a road that makes a constant angle of 5.64° with the horizontal. Find the magnitude of the truck's vertical component of displacement. Answer in units of m?

Answer 1

The vertical component of the truck's displacement as it travels 1450 m uphill at a constant incline of 5.64° is approximately 143.1 m, calculated using the sine function.

Step-by-step explanation:

To find the vertical component of the truck's displacement as it travels uphill along a road with a constant incline, you can use trigonometric functions. Specifically, you would use the sine function because you are looking for the opposite side of the right triangle formed by the truck's path and the horizontal ground.

The vertical displacement (height) can be calculated using the formula vertical displacement = total distance × sin(angle). Given that the truck travels a total distance of 1450 m and the angle of the incline is 5.64°, you can substitute these values into the formula.

So, the vertical displacement is 1450 m × sin(5.64°). Using a calculator, you will find that sin(5.64°) is approximately 0.0987. Multiplying this by the total distance gives a vertical displacement of approximately 143.1 m.

Answer 2

The vertical component of displacement of the truck traveling uphill at a 5.64° angle can be calculated by multiplying the total distance traveled (1450 m) by the sine of the angle. Use a scientific calculator to find the sine value and then multiply it to get the vertical component in meters.

Step-by-step explanation:

To find the truck's vertical component of displacement when it travels 1450 m uphill at a constant angle of 5.64°, we use trigonometric functions. The vertical component can be calculated using the sine of the angle:

Vertical displacement = Total distance × sin(angle)

Plugging in the given values:

Vertical displacement = 1450 m × sin(5.64°)

Make sure to use the angle in degrees in your calculator, or convert it to radians if necessary. After calculating, you will get the vertical component of the displacement in meters.