Vector V represents a displacement of 120 km at 29.0 degrees counterclockwise from the x axis. Write V in unit vector notation.
Express your answer using three significant figures.
V= _______ km
i know the answer should be Vx=120cos29 and Vy=120sin29 but the question requires the answer to be in form such that the answer includes variable i with an ^ above it. How do i do that?
If your using mastering physics it goes like this 105i+58.2j with the ^ over them.
having the same problem
shortcut: \hat
To write the vector V in unit vector notation, we can express it as the sum of its horizontal (Vx) and vertical (Vy) components, multiplied by their respective unit vectors.
To get the horizontal component (Vx), we can use the formula Vx = V * cos(theta), where V is the magnitude of the vector and theta is the angle counterclockwise from the x-axis. In this case, Vx = 120 km * cos(29°).
To get the vertical component (Vy), we can use the formula Vy = V * sin(theta), where V is the magnitude of the vector and theta is the angle counterclockwise from the x-axis. In this case, Vy = 120 km * sin(29°).
Now, to express these components in unit vector notation, we divide each component by the magnitude of the vector (V), and write them as a sum with their respective unit vectors.
The unit vectors in the x-direction and y-direction are denoted as i and j, respectively.
Therefore, the unit vector notation for vector V is:
V = (Vx / V) * i + (Vy / V) * j
To calculate the values for Vx and Vy, substitute the values into the equations:
Vx = 120 km * cos(29°)
Vx ≈ 107.83 km (rounding to three significant figures)
Vy = 120 km * sin(29°)
Vy ≈ 57.47 km (rounding to three significant figures)
Finally, substitute the calculated values into the unit vector notation formula:
V = (107.83 km / 120 km) * i + (57.47 km / 120 km) * j
V ≈ 0.898 i + 0.479 j (rounding to three significant figures)
Therefore, the vector V in unit vector notation is approximately V = 0.898 i + 0.479 j km.