Find the x-component of vector v⃗ = (310 m/s , 45 ∘ above +x-axis).
To find the x-component of the vector v⃗ = (310 m/s, 45° above +x-axis), we can use trigonometry.
The magnitude of the x-component can be found by multiplying the magnitude of the vector (310 m/s) by the cosine of the angle between the vector and the x-axis.
Given that the angle is 45° above the +x-axis, the angle between the vector and the x-axis becomes 90° - 45° = 45°.
Now, let's calculate the x-component using trigonometry:
x-component = magnitude of the vector * cosine of the angle
x-component = 310 m/s * cos(45°)
To evaluate this expression, we can use a scientific calculator or trigonometric table to find the cosine of 45°.
cos(45°) = 0.707 (approximately)
Therefore, the x-component of the vector v⃗ is:
x-component = 310 m/s * 0.707
x-component ≈ 219.97 m/s
So, the x-component of vector v⃗ is approximately 219.97 m/s.
as always, the x-component of v is v cosθ.
So, plug in your numbers.