S. A person is sitting at point P on a roundabout at which is rotating about a fixed axis, o, as shown in the Figure. Th

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S A Person Is Sitting At Point P On A Roundabout At Which Is Rotating About A Fixed Axis O As Shown In The Figure Th 1 (139.39 KiB) Viewed 47 times

S. A person is sitting at point P on a roundabout at which is rotating about a fixed axis, o, as shown in the Figure. They are sitting a distance 1.3 m from the centre of the roundabout which is rotating with an angular velocity of 1.2 rad/s and decelerating at a rate of 0.05 rad/s? a. Calculate the length of time until the roundabout stops, 6 stop, and the angle (in radians) through which is has turned, stop I stop = Ostup = rad. Give your answers to 4 significant figures. (4 marks) b. At the initial conditions given above, and the position shown in the figure, determine the velocity, Vp, and acceleration, ap, of the person. it jm/s. ap = it jm/s2 Give your answers to 4 significant figures. (4 marks) C. The person is throwing a ball from the roundabout such that, as viewed by the person on the roundabout, the ball has velocity VB = 4.5 m/s and acceleration ag = 9.5 m/s2 directly away from the centre of the roundabout towards A when their arm reaches its full extension of 0.5 m. Consider a local frame of reference attached to the rotating roundabout with an origin at P. Vp = i. Find the relative position of the ball as seen by the person, (rb\P)xxx i + jm. Give your answer to 4 significant figures. (TB\P)xy: (1 mark) ii. Find the relative velocity of the ball as seen by the person, (VB|P) xyz (VB|P) XYZ i + jm/s. Give your answer to 4 significant figures. = (1 mark) iii. Find the relative acceleration of the ball as seen by the person, (aB|P)xyz (ab|p) xya i + jm/s2 Give your answer to 4 significant figures. =
(26\P) xyz = (1 mark) iii. Find the relative acceleration of the ball as seen by the person, (a8|P)xyz i + j m/s2 Give your answer to 4 significant figures. (1 mark) iv. Determine the vector representing the angular velocity of the roundabout, 2. 12 = k rad/s. Give your answer to 4 significant figures. (1 mark) v. Determine the vector representing the angular acceleration of the roundabout, . = k rad/s2 Give your answer to 4 significant figures. (1 mark) vi. Hence, or otherwise, calculate the velocity of the ball, vb. VB = i + jm/s. Give your answer to 4 significant figures. (2 marks) vii. Hence, or otherwise, calculate the acceleration as = i + jm/s2 Give your answer to 4 significant figures. (2 marks) d. The person on the roundabout releases the ball immediately after the instant identified above and is facing their friend who is standing at point A, 3.3 m from the centre of the roundabout. Calculate the angle that the flight of the ball makes with the positive x-direction, the distance from the ball to the friend at this instant and hence, or otherwise, calculate the closest that the ball will get to the friend if they do not move. Angle the flight of the ball makes with the x-direction = degrees. Distance from the ball to the friend when the ball is released = Closest the ball gets to the friend = Give your answers to 4 significant figures. the ball, as m. m.
d. The person on the roundabout releases the ball immediately after the instant identified above and is facing their friend who is standing at point A, 3.3 m from the centre of the roundabout. Calculate the angle that the Flight of the ball makes with the positive x-direction, the distance from the ball to the friend at this instant and hence, or otherwise, calculate the closest that the ball will get to the friend if they do not move. Angle the flight of the ball makes with the x-direction = degrees. Distance from the ball to the friend when the ball is released = Closest the ball gets to the friend = Give your answers to 4 significant figures. (3 marks) m. m. 0 А Figure - Roundabout showing the location of points A and P.