Question

Consider a horizontally oriented syringe containing water whose nozzle is located at a height of $20\text{m}$ above the ground. The diameter of the plunger is $10\text{mm}$ and the diameter of the nozzle is $5\text{mm}$. The plunger is pushed with a constant speed of $1\text{m/s}$. Horizontal range of the water stream on the ground (in meters) is

Answer 1

Let us suppose, speed with which water comes out of the nozzle is $v$ and horizontal range of water stream on the ground is $d$.
According to question:


On applying equation of continuity
$A_1{v}_1=A_2{v}_2$
$\Rightarrow \frac{\pi d_1^2}{4}{v}_1=\frac{\pi d_2^2}{4}{v}_2$
$\Rightarrow v_2={\left(\frac{d_1}{d_2}\right)}^2{v}_1$
$\Rightarrow v={\left(\frac{10}{5}\right)}^2\times 1$
$\Rightarrow v=4\text{m/s}............\left(1\right)$
For vertical motion of water, on applying
$s=ut+\frac{1}{2}a{t}^2$
Initial vertical component of velocity of water is zero
$\therefore -20=\frac{1}{2}\times -10\times t^2$
[taking downward positive]
$\Rightarrow t=2\text{s}$ ... (2)
For horizontal motion of water, range
$d=vt$
$\Rightarrow d=8\text{m}$ [from (1) and (2)]
Hence, horizontal range of water stream on the ground is $d=8\text{m}$.