how do you setup this problem? you are on an airport \"people mover,\" a conveyo

Question

how do you setup this problem?

you are on an airport "people mover," a conveyor belt going at 2.2 m/s through a level section of the terminal. A button falls off your coat and drops freely a vertical distance of 1.6 m, hitting the belt 0.57 s later.

(a) what is the magntiude and direction of the button's net displacement and instantaneous velocity right before contact with the belt from the frame of reference of the "people mover?"

(b) what is the magntiude and direction of the button's net displacement and instantaneous velocity right before contact with the belt from the frame of reference of the airport terminal?

(c) As it falls, what is the button's acceleration in each of the different frames?

Explanation / Answer

a) with respect to the people mover the button only has vertical acceleration and velocity:

displacemetnt = 1.6 m vertially down

v = u + at

=> v = 0 + 9.8*0.57

=> v =5.586 m/s in vertically down direction

b) wrt airport terminal:

displacement(vertially down) = 1.6 m

displacemnt (horizontal) = 2.2*0.57 = 1.254 m

thus total displacement = sqrt((1.6*1.6)+(1.254*1.254)) = 2.0328590703735466 m

direction = atan(1.254/1.6) = 38.087573798048 degrees down with vertical

v(vertically down) = 5.586 m/s

v (horizontal) = 2.2 m/sec

thus total velocity:

V = sqrt((5.586*5.586)+(2.2*2.2) )= 6.0036152441674675 m/s

direction = atan(2.2/5.586) = 21.49659101741 degrees down with vertical

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