To review the solution to a similar problem, consult Interactive Solution 1.43. The magnitude of a force vector is 87.4 newtons (N). The x component of this vector is directed along the x axis and has a magnitude of 72.1 N. The y component points along the y axis. (a) Find the angle between and the x axis. (b) Find the component of along the y axis.

(a) 34.4°

(b) 49.4 N

Explanation:

(a) From the diagram,

Amgle between the x axis can be calculated as,

cosΘ = adjacent/hypoteneous

cosΘ = 72.1/87.4

cosΘ = 0.8249

Θ = cos⁻¹(0.8249)

Θ = 34.4°.

Hence the angle between the x axis is 34.4°

(b) To find the component along the y axis we make use of pythagoras theorem.

a² = b²+c²................... Equation 1

Where a = 87.4 N, b = 72.1 N, c = y.

Substitute  these values into equation 1

87.4² = 72.1² + y²

y² = 87.4²-72.1²

y² = 2440.35

y = √(2440.35)

y = 49.4 N

Answertraveling around a circular trackexplanation"traveling around a circular track" is the best answer as you could be traveling around a circular track at a constant speed. your velocity would therefore have the same magnitude but will always be constantly direction. since acceleration is the rate of change of velocity, the rate of change will only involve the direction of velocity and not the magnitude.wrong choices: "an object at rest" does not accelerate at all"increasing speed while traveling around a curve" means that the acceleration will not be constant due to only change in direction; it will be constant due to both magnitude and direction"an object in free fall" does not necessarily change direction