A balloon is flying up with a velocity of 5 m/s. at a height of 100 m a stone is dropped from it . at the instant the stone reaches the ground level the height of balloon will be ?

options :-
1. 25 m
2. 0 m
3. 125 m
4. 100 m
please answer with full explanation

2 Answers
Aug 7, 2017

Answer:

(C) #125# #"m"#

Explanation:

Well, we're given that a stone is dropped from a balloon at height #y = 100# #"m"# We're also given that the balloon (and I'll assume the rock as well) is traveling vertically upward at a constant #5# #"m/s"#.

What we can do first is find the time it takes the rock to reach the ground (i.e. height #y = 0#), using the equation

#ul(y = y_0 + v_(0y)t - 1/2g t^2#

where

  • #y# is the height at time #t# (#0#, ground-level)

  • #y_0# is the initial height (#100# #"m"#)

  • #v_(0y)# is the initial velocity (#5# #"m/s"# because it was traveling with the balloon)

  • #t# is the time (what we're trying to find)

  • #g# is the acceleration due to gravity (#9.81# #"m/s"^2#)

Let's solve the above equation for our unknown variable, #t# (using quadratic formula):

#t = (-v_(0y) +-sqrt((v_(0y))^2 - 4(-1/2g)(y_0 - y)))/(2(1/2g))#

(the #y_0 - y# is there because we had to move #y# to the right side so that #0# was left on the other side)

Plugging in known values:

#t = (-5color(white)(l)"m/s" +-sqrt((5color(white)(l)"m/s")^2 - 2(-9.81color(white)(l)"m/s"^2)(100color(white)(l)"m" - 0)))/(9.81color(white)(l)"m/s"^2)#

#= color(red)(ul(-3.92color(white)(l)"s")#

#= color(red)(ul(4.94color(white)(l)"s")#

We take the positive solution, so

#color(red)(ulbar(|stackrel(" ")(" "t = 4.94color(white)(l)"s"" ")|)#

Now what we do is find the position of the balloon at this time, using the equation

#ul(y = y_0 + v_(0y)t#

We have

  • #y = ?#

  • #y_0 = 100# #"m"#

  • #v_(0y) = 5# #"m/s"#

  • #t = color(red)(4.94color(white)(l)"s"#

Plugging these in:

#y = 100color(white)(l)"m" + (5color(white)(l)"m/s")(color(red)(4.94color(white)(l)"s")) = color(blue)(ulbar(|stackrel(" ")(" "124.94color(white)(l)"m"" ")|)#

Thus, it seems as if option (3) is correct.

Answer:

answer is
The ballon will move more 25 m
So Total height = (100+25)=125 m

Explanation:

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