A block of ice starts slilding down from the top of an inclined roof of a house along a line of the greatest slope. The inclination of the roof with the horizontal is 30^(@). The height of the highest and lowest points of the roof are 8.1 m and 5.6 m respectivley. At what horizontal distance from the lowest point will the block hit the ground? Neglect air friction [g=9.8m//s^(2)]

A block of ice starts slilding down from the top of an inclined roof o

1.	A block of ice starts slilding down from the top of an inclined roof of a house along a line of the greatest slope. The inclination of the roof with the horizontal is 30^(@). The height of the highest and lowest points of the roof are 8.1 m and 5.6 m respectivley. At what horizontal distance from the lowest point will the block hit the ground? Neglect air friction [g=9.8m//s^(2)]
Answer» Solution :Acceleration of the block along the greatest slope in equal to `a=g sin 30^(@)` Distance TRAVELLED by the block along the greatest slope is equal to `S=((8.1-5.6))/(sin 30^(@))=5m` If u be the speed of the block when it is just abou to LEAVE the roof then `u^(2)=0+2gsin 30^(@)xx5impliesu=7m//s` If t be the TIME taken on hit the ground then `5.6=u sin 30^(@)t+1/2"gt"^(2)=7/2t+1/2xx9.8t^(2)` `implies7t^(2)+5t-8=0` `t=(-5+-sqrt(25-(4)(7)xx(-8)))/(2xx7)` `impliest=(-5+-15.78)/14s`, -ve value is to be rejected , i.e. `t=(-5+15.78)/14=0.77` SEC Horizontal distance travelled is equal to `x=u cos 30^(@)t=(7sqrt(3))/2xx10.78/14mimpliesx=4.67m`