A wet open umbrella is held vertical and it whirled about the handle at a uniform rate of $21$ revolutions in $44\, s$. If the rim of the umbrella is a circle of $1\, m$ in diameter and the height of the rim above the flour is $4.9\, m$, the locus of the drop is a circle of radius:
From equation of motion $h=u t+\frac{1}{2} g t^{2}$
where $u$ is initial velocity and $t$ is time. Since, $u=0$ $\therefore t=\sqrt{\frac{2 h}{g}}=\sqrt{\frac{2 \times 4.9}{9.8}}=1 s$ The horizontal range of the drop $=x$, then $x=\left(\frac{v_{t}}{0}\right) t$ Also, $\omega=\frac{\Delta \theta}{\Delta t}=\frac{21 \times 2 \pi}{44}=3 \,rad / s$ Tangential speed $v_{t}=r \omega$ $=0.5 \times 3 \times 1.5 \,m / s$ $\therefore x=1.5 \times 1=1.5 m$ Locus of drop $=\sqrt{x^{2}+r^{2}}$ $=\sqrt{(1.5)^{2}+(0.5)^{2}}$ $=\sqrt{2.5} \,m$
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
v = final velocity of the particle
u = initial velocity of the particle
s = displacement of the particle
a = acceleration of the particle
t = the time interval in which the particle is in consideration
