Question

Find how the horizontal drift of the balloon $x$ depend on the height of ascent $y$.

• A. $\left(\frac{a}{v_0}\right)y^2$
• B. $\left(\frac{2a}{v_0}\right)y^2$
• C. $\left(\frac{3a}{2v_0}\right)y^2$
• D. $\left(\frac{a}{2v_0}\right)y^2$

Answer 1

Answer: (D)

$\left(\frac{a}{2v_0}\right)y^2$

$V_x=ay\&V_y=V_o\frac{dx}{dt}=ay\&\frac{dy}{dt}=V_o\frac{dx}{dy}=\frac{ay}{V_o}dx=\left(\frac{a}{V_o}\right)ydy$

Integrating both sides we get,
$x=\left(\frac{a}{2V_o}\right)y^2$