a truck travels up a hill with a 12% incline. the truck has a constnt speed of 22m/s. what is the horizontal componet of the reucks velocity
Ok, wondering what 12 percent means, assuming it means tangent Theta= 12/100=.12
then if you draw a right triangle, with the horizontal side 100, the opposite side 12, then the hypotenuse must be sqrt (100^2+12^2)= sqrt(10144)=101.7
so the cosine of that angle is
= 100/101.7=.983
so the horizontal velocity=22*.983
Now the big question: did you mean 12% or did you mean 12 degrees.
To find the horizontal component of the truck's velocity, we need to use trigonometry. Since the truck is traveling up a hill with a 12% incline, we can consider this incline as a right triangle.
Let's assign the given values to the right triangle:
- The height of the triangle (opposite to the incline) is 12 units.
- The base of the triangle (adjacent to the incline) is the horizontal component of the truck's velocity, which we need to find.
- The hypotenuse of the triangle is the speed of the truck (22 m/s).
Using the Pythagorean theorem, we can find the length of the base of the triangle (horizontal component of the truck's velocity). The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's solve for the base (horizontal component):
base^2 + 12^2 = 22^2
Simplifying the equation:
base^2 + 144 = 484
Subtracting 144 from both sides:
base^2 = 484 - 144
base^2 = 340
Taking the square root of both sides:
base = sqrt(340)
Evaluating the square root:
base ≈ 18.44 m/s
Therefore, the horizontal component of the truck's velocity is approximately 18.44 m/s.