A truck travels up a hill with a 7.2◦ incline.
The truck has a constant speed of 19 m/s.
What is the horizontal component of the
truck’s velocity?
Answer in units of m/s.
To find the horizontal component of the truck's velocity, we need to determine the effect of the incline on the truck's motion.
The incline can be considered as a right-angled triangle, where the incline angle is 7.2°. The horizontal component of the truck's velocity will remain the same because the incline does not affect it.
Therefore, the horizontal component of the truck's velocity will be equal to its constant speed of 19 m/s.
Answer: The horizontal component of the truck's velocity is 19 m/s.
To find the horizontal component of the truck's velocity, we need to use trigonometry. We can use the concept of the incline to find the angle between the incline and the horizontal direction.
The angle of incline is given as 7.2 degrees. This angle is the angle between the incline and the horizontal direction.
Now, we can use the trigonometric function Cosine (cos) to find the horizontal component of the velocity. The cosine function relates the adjacent side of a right triangle to the hypotenuse. Since the adjacent side is the horizontal component of the velocity and the hypotenuse is the magnitude of the velocity, we have:
cos(angle) = adjacent/hypotenuse
Substituting the given values into the equation, we get:
cos(7.2 degrees) = adjacent/19 m/s
Now, solve for the adjacent side (horizontal component):
adjacent = cos(7.2 degrees) * 19 m/s
Using a calculator, we find:
adjacent ≈ 18.83 m/s
Therefore, the horizontal component of the truck's velocity is approximately 18.83 m/s.
What is 19*cosine7.2
These relationships are fundamental, you need to get them down immediately.