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A ballis thrown form theorigin in the x - y planewithvelocity 28.28m/s at an angle 45^(@) to the x-axis. At the sameinstanta trolley alsostarts movingwith uniform velocityof 10 m/s alongthe positivex-axis . Initially rear end of the trolley is locatedat 38m from the origin. Determinethe timeposition at whichthe ball hitsthe trolley. |
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Answer» Solution :Let t be the instantat whichthe ball hits rear face B ofthe trolley. Then`(v_(0) cos 45^(@) - u_(0))t= 38` (or) `t = (38)/(v_(0) cos 45^(@)-u_(0)) = (38)/(28.28 cos 45^(@) -10) = 3.8s` At t =3.8s , the y - coordinate of the ball is . `y = (v_(0) sin 45^(@)) t - (1)/(2) "gt"^(2) = 20T - 5t^(2)` (or) `y= 20(3.8) - 5(3.8)^(2) = 3.8m` Since`3.8 gt 2m,` therefore , the ball cannothit the rear face of the trolley. Now , we assume thatthe ball hitsthe topface BC ofthe trolley , and let t be that instnat . Then ` y = 2=20 .t^(2) or t^(2) - 4t . + 0.4 = 0 : t = 3.9s` Let d be the DISTANCEFROM the pointB at whichthe ballhits the trolley. Then , `d = (v_(0) cos 45^(@) - u_(0)) (t-t) = (20-10)(3.9-3.8)= 1m` 
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