The angular speed of a point on a planet is [tex]$\frac{3 x}{10}$[/tex] radian per hour. The equator lies on a circle of radius approximately 4000 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 $\square$ miles per hour.
(Round to the nearest whole number as needed)
Answer (1)
To find the linear velocity of a point on the equator of a planet, given the angular speed and the radius of the equator, we can use the relationship between linear velocity v and angular speed Ο . This relationship is given by:
v = Ο Γ r
where:
v is the linear velocity,
Ο is the angular speed,
r is the radius of the circle.
Given:
Angular speed Ο = 10 3 x β radian per hour
Radius r β 4000 miles
Calculation:
Substitute the values into the formula:
v = ( 10 3 x β ) Γ 4000
v = 4000 Γ 10 3 x β
v = 400 Γ 3 x
v = 1200 x
Since the question asks for the linear velocity in miles per hour, and to round to the nearest whole number, it's important to notice that the exact value of x isnβt provided in this specific case. Hence, assuming x is a constant or a known value, the linear velocity expressed as a multiplication of 1200 by this variable x provides an answer based on x . However, in a complete scenario with a given x , we'd just substitute the value and compute accordingly.
Therefore, if you have a specific value for x , substitute it into the equation v = 1200 x to find the exact linear velocity in miles per hour. If rounding is necessary, round to the nearest whole number per the problem's requirements.
