Question

# A balloon starts rising from the ground with an acceleration of $$1.25 \ m/s^2$$. After 8 seconds, a stone is released from the balloon. After releasing, the stone will

A
cover a distance of 40 m till it strikes the ground.
B
have a displacement of 50 m till it reaches the ground
C
reach the ground in 4 seconds.
D
begin to move down instantaneously

Solution

## The correct option is C reach the ground in 4 seconds.The velocity of balloon at time $$t=8$$sec$$v=u+at$$Initial velocity$$=u=0$$Acceleration$$=a=1.25㎧$$$$\therefore v=at$$$$=1.25\times 8$$$$v=10㎧$$To find distance$$2as={ v }^{ 2 }-{ u }^{ 2 }$$$$\therefore S=\cfrac { { v }^{ 2 }-{ u }^{ 2 } }{ 2a }$$$$=\cfrac { 100 }{ 2\times 1.25 }$$$$\therefore S=40m$$After stone release it will cover same distance in opposite direction$$\therefore S=-40m$$Free fall of motion$$\therefore S=ut-\cfrac { 1 }{ 2 } g{ t }^{ 2 }$$$$-40=10t-5{ t }^{ 2 }$$On solving we get two values of t$$t=-2$$ and $$t=4$$Time cannot be negative$$\therefore$$ stone will reach the gound in $$4$$ secPhysics

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