Find how far runners travel on a circular track (trig)

Question

-How far has each runner traveled after 8 seconds? Though I just had to convert the rad/sec to rev/sec to get yards then multiply that by 8 seconds, but that isnt correct.

• Find the angle θ, in radians, swept out by for each after t seconds. Dont know how to do this part at all

Answer 1

The formula we need to use is $v=\omega r$ where

• $v$ is the linear speed of the runner
• $\omega$ is the angular speed
• $r$ is the radius of the circular track

We also need to make use of the following variables

• $s$ is the distance
• $t$ is the time which is given as $8$ seconds

Michael: $$v=(0.024)(110)=2.64 \text{ yd/s}$$ $$s=vt=(2.64)(8)=21.12 \text{ yd}$$ Tiffany: $$v=(0.03)(110)=3.30 \text{ yd/s}$$ $$s=vt=(3.30)(8)=26.40 \text{ yd}$$

Answer 2

Michael is running at $0.024$ rad/sec. The angle he covers is measured in radians, and the speed given is given in radians per second. Multiplying his angular speed with the time will give you the angular distance covered. $0.024 \frac{rad}{sec} * t sec = 0.024 t \frac{sec}{sec}=0.024t$ which means that for Michael his angular distance covered is $0.024t$ radians.

Answer 3

Running $x$ rad is equivalent to running $xr$ yards. Using this you can get the speed of both runners.