Answer

Verified

383.4k+ views

**Hint:**Consider a balloon having horizontal component of velocity as ${V_x} = ay$ where a is a constant and y is the height of ascent. Let the ascension rate be equal to ${V_0}$ .Now try to determine how the horizontal drift depends on the height of the ascent.

**Complete step by step answer:**

${V_x} = ay$ ………………(1)

(where${V_x}$ is the Horizontal component of velocity a is constant and y is the height of ascent)

Rate of ascension is given by the equation ${V_0} = \dfrac{{dy}}{{dt}}$ rearranging the above equation we get $dy = {V_0}dt$

Integrating both sides

Put this in equation 1

$\int {dy} = \int {{V_0}dt} = y = {V_0}t$

Now we know the horizontal component of velocity is given by the equation ${V_x} = ay$, we know that ${V_x}$ is the derivative of displacement in x axis with respect to time

${V_x} = \dfrac{{dx}}{{dt}} = ay$

Again by rearranging the above equation it can be written as $dx = aydt$

From equation number 1 we already got value of $y = {V_0}t$ ,Substitute it and then integrate both sides we get,

$dx = aydt = a{V_0}tdt$

$\int {dx = \int {a{V_0}tdt = a{V_0}\int {tdt = a{V_0}\dfrac{{{t^2}}}{2}} } } $

Since ${V_0}t = y$ we can substitute it in the equation then will get,

$x = a{V_0}\dfrac{{{t^2}}}{2} \\

\therefore x= \left( {\dfrac{a}{{2{V_0}}}} \right){y^2}$

**Hence our answer is option D.**

**Note:**First try to find out the equation for horizontal component of velocity and ascension rate then try to integrate and obtain value of y using the value of y try to find value of x or horizontal drift by integrating the obtained equation. Ascension rate is the rate at which an object rises in gas or liquid. It determines how fast the object moves upward.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Summary of the poem Where the Mind is Without Fear class 8 english CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE