First slide

Motion in a plane

Question

A balloon starts rising from the surface of earth. The ascent rate is constant and equal to $v_{0}$ . Due to wind the balloon gathers the horizontal velocity component $v_{x}$ = Ay. While A is constant and if y is the height of ascent, the horizontal drift of the balloon is:

Difficult

A

$\frac{A y^{2}}{2 v_{0}}$
B

$\frac{A y^{2}}{v_{0}}$
C

$\frac{A y^{2}}{2 v_{0}^{2}}$
D

$\frac{A y}{2 v_{0}}$

Solution

$v e r t i c a l d i s p l a c m e n t y = v_{0} t,; t = \frac{y}{v_{0}} h o r i z o n t a l d i s p l a c e m e n t x = \int v_{x} d t = \int A y d t = \int A v_{0} t d t = \frac{A v_{0} t^{2}}{2} = \frac{A v_{0} {(\frac{y}{v_{0}})}^{2}}{2} = \frac{A y^{2}}{2 v_{0}}$

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