Question

the angular speed of a point on a planet is $\frac{9pi}{10}$ radian per hour. the equator lies on a circle of radius approximately 2000 miles. find the linear velocity, in miles per hour, of a point on the equator. the linear speed of a point on the equator is approximately miles per hour (round to the nearest whole number as needed.)

Explanation:

Step1: Recall the linear - velocity formula

The formula for linear velocity $v$ in terms of angular velocity $\omega$ and radius $r$ is $v = r\omega$.

Step2: Identify the values of $r$ and $\omega$

We are given that $r = 2000$ miles and $\omega=\frac{9\pi}{10}$ radians per hour.

Step3: Substitute the values into the formula

$v=r\omega=2000\times\frac{9\pi}{10}$.

Step4: Simplify the expression

$v = 200\times9\pi=1800\pi$.

Step5: Calculate the numerical value

$v\approx1800\times 3.14159 = 5654.862$.

Step6: Round to the nearest whole number

$v\approx5655$.

Answer:

5655