The three vectors in the figure below have magnitudes a = 2.45 m, b = 3.15 m, and c = 15.0 m and angle θ = 36.5°
find x component of vector a
To find the x component of vector a, we need to find the projection of vector a onto the x-axis.
The x component of vector a can be calculated using the formula:
a_x = a * cos(θ)
Given that the magnitude of vector a is a = 2.45 m and the angle θ = 36.5°, we can substitute these values into the formula:
a_x = 2.45 m * cos(36.5°)
Using a calculator, we can evaluate the expression:
a_x ≈ 2.45 m * 0.7986
a_x ≈ 1.957 m
Therefore, the x component of vector a is approximately 1.957 m.
To find the x component of vector a, we can use the magnitude of vector a (a = 2.45 m) and the angle θ (θ = 36.5°).
The x component (a_x) can be calculated using the formula:
a_x = a * cos(θ)
First, we need to convert the angle from degrees to radians because most programming languages and calculators use radians for trigonometric functions. We can use the following conversion formula:
radians = degrees * (π/180)
So, we need to convert the angle θ from degrees to radians:
θ_radians = 36.5° * (π/180) ≈ 0.6362 radians
Now, we can calculate the x component (a_x):
a_x = 2.45 m * cos(0.6362 radians)
Use a calculator or a programming language with trigonometric functions to evaluate the cosine of 0.6362 radians and multiply it by 2.45 m.
a_x ≈ 2.45 m * cos(0.6362 radians) ≈ 2.45 m * 0.8047 ≈ 1.972 m
Therefore, the x component of vector a is approximately 1.972 m.