A truck travels 1450 m uphill along a road that makes a constant angle of 4.5◦ with the horizontal. Find the magnitude of the truck’s horizontal component of displacement.
Find the magnitude of the truck’s vertical component of displacement.
To find the magnitude of the truck's horizontal component of displacement, we need to use trigonometry.
The horizontal component of displacement can be determined using the formula:
horizontal component = hypotenuse * cos(angle)
In this case, the hypotenuse represents the total displacement of the truck, which is given as 1450 m. The angle is given as 4.5°.
Step 1: Convert the angle from degrees to radians.
To use the trigonometric functions, we need to convert the angle from degrees to radians since most mathematical functions use radians as the unit of measurement.
To convert degrees to radians, we use the following formula:
radians = degrees * (π/180)
Using this formula, we can convert the angle:
angle_radians = 4.5 * (π/180)
Step 2: Calculate the horizontal component of displacement.
horizontal_component = 1450 * cos(angle_radians)
Now we can solve for the horizontal_component using a scientific calculator or math software.
The calculation gives us the magnitude of the truck's horizontal component of displacement.