A) 10 m, 25 m
B) 5 m, 137.1 m
C) 15 m, 56 m
D) 15 m, 25 m
Correct Answer: C
Solution :
Velocity of balloon at t = 2 s is \[v=0+5\times 2=10m/s\] Height of balloon when ball has been drooped \[h=\frac{1}{2}\times 5\times {{2}^{2}}=10m\]from this instant the motion of ball is under gravity, having initial velocity same as that of balloon. Maximum height reached from ground \[=10\times \frac{{{u}^{2}}}{2g}\]\[=10\times \frac{{{(10)}^{2}}}{2\times 10}=15m\] Time taken by ball to reach ground is given by Equation \[s=ut+\frac{1}{2}g{{t}^{2}},\]take up as positive \[\Rightarrow \]\[-10=10\times t-\frac{1}{2}\times 10{{t}^{2}}\]\[\Rightarrow \]\[{{t}^{2}}-2t-2=0\] \[t=2.732,-0.732\]negative time has no meaning. In this time the balloon will reach at a height of \[h=0+\frac{1}{2}\times a\times {{(t+2)}^{2}}\] \[=\frac{1}{2}\times 5\times {{(4.732)}^{2}}\]\[=56m\]You need to login to perform this action.
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