# 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

Aug 7, 2017

#### Answer:

(C) $125$ $\text{m}$

#### Explanation:

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

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 ($100$ $\text{m}$)

• ${v}_{0 y}$ is the initial velocity ($5$ $\text{m/s}$ because it was traveling with the balloon)

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

• $g$ is the acceleration due to gravity ($9.81$ ${\text{m/s}}^{2}$)

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

$t = \frac{- {v}_{0 y} \pm \sqrt{{\left({v}_{0 y}\right)}^{2} - 4 \left(- \frac{1}{2} g\right) \left({y}_{0} - y\right)}}{2 \left(\frac{1}{2} g\right)}$

(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:

$t = \left(- 5 \textcolor{w h i t e}{l} {\text{m/s" +-sqrt((5color(white)(l)"m/s")^2 - 2(-9.81color(white)(l)"m/s"^2)(100color(white)(l)"m" - 0)))/(9.81color(white)(l)"m/s}}^{2}\right)$

= 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 = ?

• ${y}_{0} = 100$ $\text{m}$

• ${v}_{0 y} = 5$ $\text{m/s}$

• 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.

Aug 7, 2017

#### Answer:

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

#### Explanation: Enjoy physics🙌🙌🙌:-) :-) :-)