a truck drives up a hill with a 15 degree incline. if the truck has a constant speed of 22 m/s, what are the horizontal and vertical components of the trucks velocity?
Kayla: MrPhysics erred, and got the forces reversed.
Horizontal is the cosine function
Vertical is the sine function.
horizontal velocity = 22sin(15)
vertical velocity = 22cos(15)
thank you so so so so much !
To find the horizontal and vertical components of the truck's velocity, we can use trigonometry.
The horizontal component of velocity (Vx) represents the speed of the truck in the direction parallel to the ground, whereas the vertical component of velocity (Vy) represents the speed of the truck in the direction perpendicular to the ground.
Given:
Speed of the truck (V) = 22 m/s
Incline angle (θ) = 15 degrees
To find Vx, we need to find the component of V that is parallel to the ground. This can be calculated using the cosine function:
Vx = V * cos(θ)
Substituting the given values:
Vx = 22 m/s * cos(15 degrees)
To find Vy, we need to find the component of V that is perpendicular to the ground. This can be calculated using the sine function:
Vy = V * sin(θ)
Substituting the given values:
Vy = 22 m/s * sin(15 degrees)
Now, let's calculate Vx and Vy.
Vx = 22 m/s * cos(15 degrees)
≈ 21.109 m/s
Vy = 22 m/s * sin(15 degrees)
≈ 5.693 m/s
Therefore, the horizontal component of the truck's velocity (Vx) is approximately 21.109 m/s, and the vertical component of the truck's velocity (Vy) is approximately 5.693 m/s.