Rolling Marble on Table Top Points:4 A marble is rolling on top of a table, goin

Question

Rolling Marble on Table Top Points:4 A marble is rolling on top of a table, going along the +x-axis. Its positions at a fixed time interval, At- 0.19 s, is shown with x's on the g below. raph 65 60 40 35 30 25 20 10 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100105110 Horizontal position, x, (cm) What is the speed of the marble just before it rolls off the table? Submit Answe Tries 0/10 How long does it take for the marble to fall from the top of the table to the floor? Where along the x-axis does the marble hit the floor? Neglect any air resistance. NOTE: Both answers must be correct to get credit. werTries 0/10 At what angle does the marble hit the floor? Use +x-axis to be 0 degree going counter-clockwise Submit AnswerTries 0/10 What is the position of the marble 0.279 s after it rolls over the edge? Put the x coordinate in the first box below and the y-coordinate in the second box. Submit Answer Tries 0/10

Explanation / Answer

along horizontal

during the fixed time interval

distance travelled on table x = 70 cm = 0.70 m

time taken t = 4*0.19 = 0.76 s

speed of marble just before it rolls vx = x/t = 0.7/0.76 = 0.92 m/s

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along vertical

initial position y0 = 60 cm = 0.6 m

acceleration ay = -g = -9.8 m/s^2

initial velocity voy = 0

final position y = 0

y - y0 = voy*t + (1/2)*ay*t^2

0 - 0.6 = 0 - (1/2)*9.8*t^2

time taken t = 0.35 s <<-----ANSWER

along horizontal

acceleration ax = 0

x - 0.75 = vx*t + (1/2)*ax*t^2

x- 0.75 = 0.92*0.35

x = 1.072 m = 107.2 cm <<---------ANSWER

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along vertical

final velocity before hitting

vy = voy + ay*t

vy = 0 - 9.8*0.35 = -3.43 m/s

vx = 0.92 m/s

tantheta = vy/vx

theta = tan^-1(-3.43/0.92) = +285 degrees

===========================================

along horizontal

x = vx*t = 0.92*0.279 = 0.257 m

along vertical

y - y0 = voy*t + (1/2)*ay*t^2

y - 0.6 = 0 - (1/2)*9.8*0.279^2

y = 0.218 m

(x , y ) = ( 0.257 m , 0.218 m )

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