A truck travels up a hill with a 10
◦
incline.
The truck has a constant speed of 21 m/s.
What is the horizontal component of the
truck’s velocity?
Answer in units of m/s
What is the vertical component of the truck’s
velocity?
Answer in units of m/s
To find the horizontal and vertical components of the truck's velocity, we can use some trigonometry.
Given:
- Incline angle: 10°
- Truck speed: 21 m/s
Horizontal Component of Velocity:
The horizontal component of velocity represents the part of the velocity that is parallel to the ground. To find this component, we need to find the adjacent side of the right triangle formed.
Using trigonometry, we can use the cosine function:
cos(angle) = adjacent/hypotenuse
In this case, the adjacent side represents the horizontal component of the velocity, and the hypotenuse represents the total velocity of the truck.
cos(10°) = adjacent/21 m/s
Now we can solve for the adjacent side:
adjacent = cos(10°) * 21 m/s
Calculating:
adjacent = cos(10°) * 21 m/s = 20.26 m/s
Therefore, the horizontal component of the truck's velocity is approximately 20.26 m/s.
Vertical Component of Velocity:
The vertical component of velocity represents the part of the velocity that is perpendicular to the ground, which is affected by gravity. To find this component, we need to find the opposite side of the right triangle formed.
Using trigonometry, we can use the sine function:
sin(angle) = opposite/hypotenuse
In this case, the opposite side represents the vertical component of the velocity, and the hypotenuse represents the total velocity of the truck.
sin(10°) = opposite/21 m/s
Now we can solve for the opposite side:
opposite = sin(10°) * 21 m/s
Calculating:
opposite = sin(10°) * 21 m/s = 3.64 m/s
Therefore, the vertical component of the truck's velocity is approximately 3.64 m/s.