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A bicycle has wheels with diameter 630 mm. The center of a red reflector is on the front wheel 79 mm from the edge of the tire. If the bicycle is traveling at a speed of 1.6 meters per second, find a function for the height of the center of the red reflector at time t seconds. (Assume that at t = 0, the reflector is at its lowest height.)

User IvanH
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Answer: The reflector's height can be modeled as a function of time. The function will depend on the radius of the wheel, the distance of the reflector from the edge of the tire, and the speed of the bicycle.

Let's call the radius of the wheel r. The radius is half of the diameter, so:

r = 630 / 2 = 315 mm

Also, let's call the distance of the reflector from the edge of the tire d.

d = 79 mm

Given that the reflector is at its lowest height at t = 0, we know that at that time the center of the reflector is at a height of r + d = 315 + 79 = 394 mm.

The height of the center of the red reflector at time t seconds is given by:

h(t) = (r + d) + vt

Where v is the speed of the bicycle in meters per second, and t is the time in seconds.

Substituting the values we have:

h(t) = 394 + (1.6 x t)

So the function for the height of the center of the red reflector at time t seconds is h(t) = 394 + (1.6 x t) (in mm)

It's important to note that this function is based on the assumption that the reflector is at its lowest height at time t = 0 and that the height of the reflector increases linearly with time as the bike moves forward.

Explanation:

User Alexander Korovin
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