First slide

Question on vertical

Question

A stone is thrown vertically upward with an initial velocity $v_{0}$ . The distance travelled in time $\frac{4 v_{0}}{3 g}$ is

Moderate

A

$\frac{2 v_{0}^{2}}{3 g}$
B

$\frac{v_{0}^{2}}{3 g}$
C

$\frac{v_{0}^{2}}{2 g}$
D

$\frac{5 v_{0}^{2}}{9 g}$

Solution

$T i m e o f a s c e n t i s \frac{v_{0}}{g} g i v e n t i m e i s \frac{4 v_{0}}{3 g} t i m e f o r d o w n w a r d j o u r n e y i s \frac{4 v_{0}}{3 g} - \frac{v_{0}}{g} = \frac{v_{0}}{3 g} d i s \tan c e t r a v e l l e d i n \frac{v_{0}}{3 g} w h i l e f a l l i n g = \frac{1}{2} g {(\frac{v_{0}}{3 g})}^{2} = \frac{v_{0}^{2}}{18 g} s o t o t a l d i s \tan c e t r a v e l l e d i s \frac{v_{0}^{2}}{18 g} + \frac{v_{0}^{2}}{2 g} = \frac{5 v_{0}^{2}}{9 g}$

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