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Two balloons are simultaneously released from two buildings $A$ and $B$ . Balloon from $A$ rises with constant velocity $10 m s^{- 1},$ while the other one rises with constant velocity of $20 m s^{- 1} .$ 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 ' $t$ ' (in seconds) the balloons collide.

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$t = 5 \sec .$

difference in height of buildings is 100 m

difference in height of buildings is $500 m$

$t = 10 \sec$

answer is B, D.

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Detailed Solution

for $A : y_{A} = 10 t; x_{A} = \int_{0}^{t} 0.5 \times 10 t d t = \frac{5 t^{2}}{2}$
for $B : y_{B} = 20 t; x_{B} = \int_{0}^{t} 0.5 \times 20 t d t = 5 t^{2}$
$x_{B} = x_{A} + 250$
Difference of height of tower $= y_{B} = y_{A}$

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