A foot pump is depicted in the figure. At the given time instant, link ABC is rotating anti-clockwise about point C at a constant rate of 30 rad/s. The rotation of link ABC is determining the rate of rotation of link DE which is pivoted at point D. The pump collar (green box) is attached to link ABC by means of a pin joint at point F, and the piston (blue) is able to slide inside the collar. For the given time instant point F (a point on link ABC) lies directly beneath point E (a point on link DE). B (Figure not to scale!) WABC WDE For the instant shown: a) Using a suitable coordinate system find the velocity vector of point B using the analytical method [3 marks) b) Draw the velocity diagram to determine the velocity of piston E relative to point F on the collar. Label all points and lines. [7 marks Suggested scale: 1 mm = 0.05 m/s, pole point: right-centre of page. c) Compute the angular acceleration (magnitude and direction) of link DE using the ana- lytical method. For this question, assume that wpE = 6 rad/s. (10 marks Substitute numbers at the very end! Given: AB = 0.087 m, BC = 0.123 m, FC = 0.084 m, DE = 0.138 m, EG = 0.051 m, a = 36, B = 73, WABC = 30 rad/s. A foot pump is depicted in the figure. At the given time instant, link ABC is rotating anti-clockwise about point C at a constant rate of 30 rad/s. The rotation of link ABC is determining the rate of rotation of link DE which is pivoted at point D. The pump collar (green box) is attached to link ABC by means of a pin joint at point F, and the piston (blue) is able to slide inside the collar. For the given time instant point F (a point on link ABC) lies directly beneath point E (a point on link DE). B (Figure not to scale!) WABC WDE For the instant shown: a) Using a suitable coordinate system find the velocity vector of point B using the analytical method [3 marks) b) Draw the velocity diagram to determine the velocity of piston E relative to point F on the collar. Label all points and lines. [7 marks Suggested scale: 1 mm = 0.05 m/s, pole point: right-centre of page. c) Compute the angular acceleration (magnitude and direction) of link DE using the ana- lytical method. For this question, assume that wpE = 6 rad/s. (10 marks Substitute numbers at the very end! Given: AB = 0.087 m, BC = 0.123 m, FC = 0.084 m, DE = 0.138 m, EG = 0.051 m, a = 36, B = 73, WABC = 30 rad/s