It goeas all the way around. The figure below illustrates the path of a toy race

Question

It goeas all the way around.

The figure below illustrates the path of a toy racecar that begins at (8,0) and travels d meters counter-clockwise on a circular path with an 8-meter radius. The racecar stops at the point (x, y). Define a formula that relates the horizontal component, x, (measured in radius lengths) in terms of the number of meters, d, the racecar has traveled alone the track. Define a formula that relates the vertical component, y, (measured in radius lengths) in terms of the number of meters, d, the racecar has traveled along the track. Define a formula that relates the horizontal component, x (measured in meters) in terms of the number of meters, d, the racecar has traveled along the track. Define a formula that relates the vertical component, y, (measured in meters) in terms of the number of meters, d, the racecar has traveled along the track.

Explanation / Answer

The path is along circular with radius = 8

d = distance travelled along the circular track

Hence d = arc length of the circle

If t is the angle between OX and Horizontal line,

then d = 8t (arc length formula in radians)

Hence x= 8t cos t

and y = -8t sint where t is the angle traversed

x= tcost (radius) and y = -tsint (radius)

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In metres,

x = 8t cost metres and y = -8t sint metres.

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