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A blockof icestarts slidingdown from the topof an inclinedroofof a alonga lineof the greatestslope. Theinclination of the roof withthe horizontal is 30^(@). Theheights of thehighestand lowerst points of the roof are 8.1 m and 5.6 mrespectively.Atwhathorizontal distancefrom the lowest point will the blockhitthe ground ? Neglect air friction .[g=9.8m//s^(2)]. |
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Answer» Solution :Accelerationof the block ALONGTHE greatestslope is equal to `a = g sin30^(@)` . Distancetravelled by the block along the greatestslope is equal to `S = ((8.1 - 5.6))/(sin 30^(@)) = 5m` Ifu be the speed of the blockwhen it justaboutto leavethe roofthen `u^(2) = 0+ 2 g sin 30^(@)30^(@) xx5rArru = 7 m//s` If thebe the timetaken to hitthe groundthen `5.6 = u sin 30^(@) t + (1)/(2) gt^(2)= (7)/(2)t + (1)/(2) XX 9.8 t^(2)` `rArr 7t^(2) + 5t - 8 = 0` ` t = (-5+pm sqrt(25-(4)(7)xx(8)))/(2xx7)` `rArr t = (-5pm 15.78)/(14) ` , -vevalueis to be rejected , `i.e., t = (-5+15.78)/(14) = 0.77 sec` Horizontal distancetravelled is equal to . `x = u cos 30^(@) t = (7 sqrt(3))/(2) xx (10.78)/(14) m RARRX = 4.67 m ` 
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