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

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

Explanation:

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