Question

For each of the following velocity vectors, give the vector component, the scalar component, and the magnitude. (a) v = 48.0j m/s (i) vector component (Express your answer in vector form.)

Answer 1

The vector component of the velocity is (0i + 48.0j)m/s. The scalar component is 48.0 m/s. The magnitude of the velocity is 48.0 m/s.

Step-by-step explanation:

To find the vector component of the velocity vector v = 48.0j m/s, we can use the unit vectors i and j. Since the vector is given only in the j direction, the vector component in the i direction would be zero. Therefore, the vector component of v is (0i + 48.0j)m/s.

Next, to find the scalar component of v, we isolate the magnitude of the vector component. Since the vector component in the i direction is zero, we can ignore it. The scalar component is equal to the magnitude of the vector component, which in this case is 48.0 m/s.

Finally, to find the magnitude of v, we take the square root of the sum of the squares of the components. Since the component in the i direction is zero, we only need to consider the component in the j direction. The magnitude of v is therefore the square root of (0^2 + 48.0^2) m/s, which is 48.0 m/s.

Answer 2

Obtaining the component part of the letter 'i' warns that it is the velocity is oriented on the X axis. At the same time the numeric part, in this particular case will represent the scalar part and therefore the magnitude of the vector.

The velocity is

`\vec{v} = 48.0\hat{i} \text{ m/s }`

The vector component of the velocity is

`v_x = 48.0m/s`

The scalar component of the velocity is

`v = 48.0m/s`

The magnitude of the velocity is

`v = 48.0m/s`