You are given a vector in the xy plane that has a magnitude of 85.0 units and a y component of -60.0 units. What are the two possibilities for its x component?
To find the two possibilities for the x component of the given vector, you can use the Pythagorean theorem. The Pythagorean theorem states that for a right triangle, the square of the hypotenuse (c, the magnitude of the vector in this case) is equal to the sum of the squares of the other two sides (x and y components).
Given:
Magnitude of the vector (c) = 85.0 units
Y component (y) = -60.0 units
We can use the Pythagorean theorem to find the two possibilities for the x component.
Using the Pythagorean theorem,
c^2 = x^2 + y^2
Substituting the given values,
85.0^2 = x^2 + (-60.0)^2
7225.0 = x^2 + 3600.0
Rearranging the equation,
x^2 = 7225.0 - 3600.0
x^2 = 3625.0
Taking the square root of both sides,
x = ± √3625.0
Therefore, the two possibilities for the x component of the vector are:
1. x = √3625.0
2. x = -√3625.0
To find the two possibilities for the x component, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the magnitude of the vector represents the hypotenuse, and the x and y components represent the other two sides.
Let's denote the magnitude of the vector as |V| = 85.0 units, the x component as Vx, and the y component as Vy = -60.0 units.
Using the Pythagorean theorem, we have the following equation:
|V|² = Vx² + Vy²
Substituting the given values, we get:
85.0² = Vx² + (-60.0)²
Simplifying the equation, we have:
7225.0 = Vx² + 3600.0
Rearranging the equation, we have:
Vx² = 7225.0 - 3600.0
Vx² = 3625.0
Taking the square root of both sides, we have:
Vx = ±√3625.0
Calculating the square root, we get:
Vx = ±60.208
Thus, the two possibilities for the x component are approximately +60.208 units or -60.208 units.
it can be positive or negative x
x=+- 85cosTheta
where Theta=arcsin(60/85)
i don't get what theta is
or arcsin