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A balloon starts ascending with a constant acceleration for 5 sec. A stone is thrown from the balloon and it reaches the ground in 5 sec. Calculate the velocity with which the balloon starts rising upwards. Ans :12.5 m/s

A balloon starts ascending with a constant acceleration for 5 sec. A stone is thrown from the balloon and it reaches the ground in 5 sec. Calculate the velocity with which the balloon starts rising upwards.
Ans :12.5 m/s

Grade:11

1 Answers

Arun
25750 Points
3 years ago
Analysis of situation: t = 0 is the time when the balloon started rising up. At t = 0, when the packet is dropped, the balloon is moving up with velocity v = 0 + at 
0
​ 
  = at 
0
​ 
 . Hence, initial velocity of the packet will be v 
0
​ 
 =at 
0
​ 
  (upward). As the balloon has started rising upwards with constant acceleration a, so after t 
0
​ 
  seconds, its height from the ground is y 
0
​ 
 = 
2
1
​ 
 at 
0
2
​ 
 .
For packet: s = ut - 
2
1
​ 
 gt 
2
 
⇒ − 
2
1
​ 
 at 
0
2
​ 
  = at 
0
​ 
 t− 
2
1
​ 
 gt 
2
  ⇒ gt 
2
 −2at 
0
​ 
 t−at 
0
2
​ 
 =0
Solving the quadratic equation, we get t =  
g
at 
0
​ 
 
​ 
 [1+ 
1+ 
a
g
​ 
 
​ 
 ]

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