In this problem use exact numbers (involving Squareroot, pi, etc.) rather than d

Question

In this problem use exact numbers (involving Squareroot, pi, etc.) rather than decimals; in other words, do not use a calculator for this problem. An object travels counterclockwise at constant angular velocity of 1 revolution every 8 seconds around the circle having equation x^2 + y^2 = 200. At time f = 0 it is at the right-most point, on the circle (which is on the x-axis). After 11 seconds it Hies off the circle, traveling at constant velocity along the tangent line. (You might find it useful to draw a picture showing the circle and the tangent line.) First find the radius and circumference of the circle and the speed of the object (which has constant speed, although the direction of its velocity vector changes). Also find the coordinates of the point where it flies off the circle. Then find parametric equations for the object's motion both before and after it flies off the circle, that is, both for 0 lessthanorequalto t lessthanorequalto 11 and for t lessthanorequalto 11. Please show your work clearly and neatly.

Explanation / Answer

equation of the circle is x^2 + y^2 = 200

comparing it with the general equaiton of the circle that is : (x-h)^2 + (y-k)^2 = r^2

where (h,k) is the center and r is the rdius

In our problem the center is (0,0) and the radius is sqrt(200) = 10sqrt(2)

the circumference of the circle is = 2pi*radius = 2*pi*10sqrt(2) = 20*pi*sqrt(2)

the constant angular velocity is = 1 revolution /8 seconds = 1*60/8 revolution per minute = 30/4 rpm

angular velocity in radians per second = 30/4 * 2pi/60 = pi/30 radians per second

linear velocity = radius*angular velocity= 10sqrt(2)*pi/30 = pi*sqrt(2)/3 m/sec

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.