Question: An open umbrella is held upright and rotated about the handle at a uniform rate of 21 revolution in ...

Question

An open umbrella is held upright and rotated about the handle at a uniform rate of 21 revolution in 44 s. If the rim of the umbrella is a circle of 100 cm diameter and the height of the rim above ground is 150 cm then the drops of water spinning off the rim will hit the ground at

Answer 1

Solution

Velocity of water drop.

v = rω = 0.5 × $\frac{(2\pi \times 21)}{44}$ = 1.5 ms^-1

Time taken to reach ground,

t = $\sqrt{\frac{2h}{8}} = \sqrt{\frac{2 \times 1.5}{9.8}}$ = 0.55 s

Range of drop, x = vt = 1.5 × 0.55 = 0.83 m

distance R = $\sqrt{r^{2} + x^{2}} = \sqrt{0.5^{2} + 0.83^{2}} = 0.97$ m = 97 cm