Two ballons are simultaneously released from two buildings A and B. Balloon from A rises with constant velocity `10ms^(-1)` While the other one rises with constant velocity of `20ms^(-1)` Due to wind the balloons gather horizontal velocity `V_(x)=0.5` y, where 'y' is the height from the point of release. The buildings are at a distance of `250` m & after some time 't' the balloons collide.

Options

A. `t=5`sec
B. difference in height of buildings in 100m
C. difference in height of buildings is 500
D. `t=0` sec

Answer

B, D

Explanation

`20xxt=10t+arArr10 t=a`
for B for A
`v_(n)=y/2`
`v_(n)=y/2`
`(dn)/(dt)=(20t)/2 (dn)/(dt)=(10t)/2`
`underset0oversetb intdx=underset0overset tint10t dt underset250 overset b int dx =underset0oversettint5tdt`
`b=5t^(2) b-250=(5t^(2))/2`
`5t^(2)-250=(5t^(2))/2 Rightarrow t=10& a=100`