Skateboarder S rides on a straight sidewalk (the ground)

PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

Skateboarder S rides on a straight sidewalk (the ground). Define

+x

toward the east. Let

v_{\text{SG}}

be the skateboarder’s velocity relative to the ground,

v_{\text{SF}}

the skateboarder’s velocity relative to Friend F (who may be moving), and

v_{\text{FG}}

the friend’s velocity relative to the ground. (a) Using precise verbal reasoning and symbolic algebra, derive a general relationship that connects

v_{\text{SG}}

v_{\text{SF}}

, and

v_{\text{FG}}

for one-dimensional motion. Clearly state any sign conventions or assumptions used in your derivation. (b) Friend F walks

1.0\,\text{m}\!\cdot\!\text{s}^{-1}

east relative to the ground. At the same instant Skateboarder S moves

2.0\,\text{m}\!\cdot\!\text{s}^{-1}

east relative to the ground. Use your expression from part (a) to determine the skateboarder’s velocity relative to the friend, including sign and units. (c) Consider the limiting case in which two observers move at equal speeds but in opposite directions (for example,

v_{\text{FG}}=-v_{\text{SG}}

). Use your derived expression to compute

v_{\text{SF}}

for this case and interpret the physical meaning of your result.

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