A truck travels up a hill with a 10� incline.
The truck has a constant speed of 16 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
horizonal vel=16cos10
vertical vel=16sin10
To find the horizontal and vertical components of the truck's velocity, we need to use trigonometry.
In this case, we can treat the incline of the hill as a right triangle, where the angle of incline is 10 degrees. The horizontal component of the truck's velocity is the component of its velocity that acts parallel to the ground, and the vertical component is the component that acts perpendicular to the ground.
To find the horizontal component of the truck's velocity, we can use the formula:
Horizontal component = Velocity * cos(angle)
In this case, the velocity is 16 m/s and the angle is 10 degrees. Plugging these values into the formula:
Horizontal component = 16 m/s * cos(10 degrees)
Using a calculator or a trigonometric table, we find that cos(10 degrees) is approximately 0.9848.
Horizontal component = 16 m/s * 0.9848 = 15.76 m/s
Therefore, the horizontal component of the truck's velocity is approximately 15.76 m/s.
To find the vertical component of the truck's velocity, we use a similar formula:
Vertical component = Velocity * sin(angle)
In this case, the velocity is still 16 m/s and the angle is still 10 degrees. Plugging these values into the formula:
Vertical component = 16 m/s * sin(10 degrees)
Using a calculator or a trigonometric table, we find that sin(10 degrees) is approximately 0.1736.
Vertical component = 16 m/s * 0.1736 = 2.7776 m/s
Therefore, the vertical component of the truck's velocity is approximately 2.7776 m/s.