Question

A stone is thrown vertically upwards. On its way, passes a point P with a speed $v$ and point Q is $20m$ higher than Q with a speed $\frac{\sqrt{5}}{3}v$. The value of speed: [$g=10m/s^2$]

• A. $20\sqrt{5}m/s$
• B. $15\sqrt{5}m/s$
• C. $25m/s$
• D. $30m/s$

Answer 1

The correct option is D $30m/s$

The velocity at P is V

Heigth difference is 20m

Velocity at Q $=\frac{\sqrt{4}v}{3}$

$(\frac{\sqrt{5}v}{3}{)}^2=v^2-2\times 20\times 10$

$2\times 20\times 10=v^2-\frac{5}{9}{v}^2$

$\frac{4}{9}{v}^2=2\times 20\times 10$

$\frac{2}{3}v=2\times 10$

$v=\frac{2\times 10\times 3}{2}=30m/s$