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Q.

Two balloons are simultaneously released from two buildings A and B. Balloon from A rises with constant velocity 10 ms-1, While the other one rises with constant velocity of 20 ms-1 . Due to wind the balloons gather horizontal velocity Vx = 0.5 y, where y is the height from the point of release. The buildings are at a distance of 250 m and after some time t the balloons collide. Choose the correct option(s).

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a

t = 5 sec

b

difference in height of buildings is 100 m

c

difference in height of buildings is 50 m

d

t = 10 sec

answer is B.

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Detailed Solution

yB−yA=20t−10t=10t ……..(i)Difference in the height of buildingXB−XA=∫0t 0.5yBdt−∫0t 0.5yAdt …….(ii)Separation between the buildings = 250 mHence ∫0t 0.5×20t.dt−∫0t 0.5×10t.dt=250 5∫0t t.dt=250Hence 5t22=250⇒t=10sDifference in the height of building = 10t =10×10=100mDifference in heights =y2−y1=20t−10t=100m

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Two balloons are simultaneously released from two buildings A and B. Balloon from A rises with constant velocity 10 ms-1, While the other one rises with constant velocity of 20 ms-1 . Due to wind the balloons gather horizontal velocity Vx = 0.5 y, where y is the height from the point of release. The buildings are at a distance of 250 m and after some time t the balloons collide. Choose the correct option(s).