A body falling freely from a ht. H hits an inclined plane at a ht.h As a result of this impact,the direction of the velocity of the body becomes horizontal.For what value of h:H the body will take max. time 2 reach yhe ground
For the first part body is travelling upto inclined plane with zero initial velocity and acceleration g and the distance travelled upto the plane is H-h. So t1=2(H-h)/g
For the second part body is travelling from inclined plane to the ground with zero initial velocity veritcally(since the velocity becomes horizontal after striking the plane) and travels a distance of h. So t2=2h/g
So total time taken t = 2(H-h)/g + 2h/g
For t to be maximum dt/dh = 0 implies -1/([(H-h))g] + 1/[(h)g] = 0 which gives H-h = h i.e. h:H = 1:2
Moderation Team
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18
1
(H-h/g)) +(2
(H-h)/g
