It goeas all the way around The figure below illustrates the

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.

Solution

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.