Question

Find x-component of vector v⃗ =(250m/s , 30∘ above + x-axis)

Answer 1

The x-component of the vector v⃗=(250m/s, 30° above the +x-axis) is calculated using the cosine of the angle, and it equals approximately 216.5 m/s.

Step-by-step explanation:

To find the x-component of the vector v⃗ = (250 m/s, 30° above + x-axis), we use the cosine function of the angle which refers to the adjacent side in a right-angled triangle (the x-component in this context). The formula to calculate the x-component (Vx) is:

Vx = Voo cos(θ)

where Voo is the magnitude of the initial velocity (250 m/s) and θ is the angle made with the horizontal (30°). Let's calculate Vx:

Vx = 250 m/s * cos(30°)

To get the numerical value of Vx, we use the cosine of 30 degrees, which is √3/2. Multiplying these, we get:

Vx = 250 m/s * √3/2

Vx ≈ 216.5 m/s (rounded to one decimal place)

The x-component of the velocity for the given vector is approximately 216.5 m/s.

Answer 2

We have to calculate the x- component of vector v = 250 m/s.
α = 30° ( above the x-axis ):
v x = v · cos α
v x = 250 m/s · √3/2 = 250 m/s · 0.866 = 216.5 m/s
Answer:
v x = 216.5 m/s