A) reach the ground in 4 second
B) begin to move down after being released
C) have a displacement of 50 m
D) cover a distance of 40 m in reaching the ground
Correct Answer: A
Solution :
Acceleration \[a=1.25\,m/{{s}^{2}}\] time\[t=8\,sec\] (given) Acceleration due to gravity \[g=10\,m/{{s}^{2}}\] Let the balloon be at a height h above the ground, when the stone is released from it. \[h=0\times t+\frac{1}{2}\times 1.25\,\times {{(8)}^{2}}\] \[=40\,m\] Velocity of the balloon at this instant \[\upsilon =0+1.25\times 8=10\,m/s\] For the journey of stone, let it take time t to reach the ground Now \[u=-10\,m/s,\]\[s=40m,\,g=10\,m/{{s}^{2}}\] so \[s=ut+\frac{1}{2}g{{t}^{2}}\] \[40=-10t\frac{1}{2}\times 10{{t}^{2}}\] \[{{t}^{2}}-2t-8=0\] \[(t+2)(t-4)=0\] \[t=-2\](not admissible) \[t=4\sec \] The stone takes 4 second to reach the ground.
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