No, that is incorrect.
The phrasing asks for Neil's velocity as seen by Barbara, so we need to find the relative velocity of Neil with respect to Barbara. We will use the formula V_n/b = V_n - V_b where V_n/b is Neil's velocity relative to Barbara, V_n is Neil's velocity, and V_b is Barbara's velocity.
V_n = 3.2 m/s west
V_b = 5.2 m/s south
To find the relative velocity, we subtract the two vectors:
V_n/b = V_n - V_b = 3.2 m/s west - 5.2 m/s south
This gives us a vector pointing southwest.
(a) To find the magnitude we use the Pythagorean theorem:
|V_n/b| = √((3.2 m/s)² + (5.2 m/s)²) ≈ 6.1 m/s
So, the magnitude of the relative velocity is 6.1 m/s.
(b) To find the direction relative to due west, we can find the angle formed by the x-component (west) and the resulting vector.
θ = arctan(|V_south|/|V_west|) = arctan(5.2/3.2) = arctan(1.625) ≈ 58.6°
So, the direction of Neil's velocity relative to Barbara is 58.6° south of west.
Two friends, Barbara and Neil, are out rollerblading. With respect to the ground, Barbara is skating due south at a speed of 5.2 m/s. Neil is in front of her. With respect to the ground, Neil is skating due west at a speed of 3.2 m/s. Find Neil's velocity ((a) magnitude and (b) direction relative to due west, as seen by Barbara.
With vector addition in regards to the first part of the question, would (a) = 8.4 m/s? I may not be understanding the phrasing...
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