A truck travels up a hill with a 15◦incline.The truck has a constant speed of 26 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
Vo = 26m/s @ 15o.
Xo = 26*cos15 = 25.1 m/s.
Yo = 26*sin15 = 6.73 m/s.
To find the horizontal and vertical components of the truck's velocity, we need to break down the velocity vector into its horizontal and vertical components.
Given:
Incline angle = 15 degrees
Truck's speed = 26 m/s
The horizontal component of velocity (Vx) can be found using the formula:
Vx = V * cos(θ)
Where V is the magnitude of the velocity vector and θ is the angle of inclination.
Substituting the given values:
Vx = 26 m/s * cos(15 degrees)
Calculating the horizontal component:
Vx ≈ 24.80 m/s (rounded to two decimal places)
The vertical component of velocity (Vy) can be found using the same formula, but with the sine function:
Vy = V * sin(θ)
Substituting the given values:
Vy = 26 m/s * sin(15 degrees)
Calculating the vertical component:
Vy ≈ 6.69 m/s (rounded to two decimal places)
Therefore, the horizontal component of the truck's velocity is 24.80 m/s, and the vertical component is 6.69 m/s.
To find the horizontal and vertical components of the truck's velocity, we can use trigonometric functions.
The horizontal component of the truck's velocity is the component that acts parallel to the ground, while the vertical component is the component that acts perpendicular to the ground.
Given that the truck is traveling up a hill with a 15° incline, the angle between the hill's surface and the ground is 15°.
To find the horizontal component, we can use the cosine function:
Horizontal component = Velocity × cos(angle)
= 26 m/s × cos(15°)
We can calculate this using a calculator or online trigonometric calculator. The result is:
Horizontal component ≈ 25.115 m/s
To find the vertical component, we can use the sine function:
Vertical component = Velocity × sin(angle)
= 26 m/s × sin(15°)
Again, we can calculate this using a calculator or online trigonometric calculator. The result is:
Vertical component ≈ 6.719 m/s
Therefore, the horizontal component of the truck's velocity is approximately 25.115 m/s, and the vertical component is approximately 6.719 m/s.