The nozzle diameter changed by a factor of 0.907

<h3>Further explanation</h3>
Acceleration is rate of change of velocity.


<em>a = acceleration (m / s²)v = final velocity (m / s)</em>
<em>u = initial velocity (m / s)</em>
<em>t = time taken (s)</em>
<em>d = distance (m)</em>
Let us now tackle the problem!

<u>Given:</u>
horizontal distance = x = 36.9 m
angle of projection = θ = 45°
initial height = y₁ = 8.85 m
final height = y₂ = 17.9 m
<u>Asked:</u>
ratio of nozzle diameter = d₂ : d₁ = ?
<u>Solution:</u>
<em>The motion of the water is a </em><em>parabolic motion.</em>
<em>Firstly, we will calculate the time taken for the water to reach the hotspot:</em>





<em>Next , we could calculate the initial speed (u) of the water as it leaves the nozzle:</em>








<em>Finally , we could find the ratio of the diameter by using </em><em>Continuity Equation</em><em> as follows:</em>





![\frac {d_2}{d_1} = \sqrt[4] { \frac {x - y_2} {x - y_1} }](https://tex.z-dn.net/?f=%5Cfrac%20%7Bd_2%7D%7Bd_1%7D%20%3D%20%5Csqrt%5B4%5D%20%7B%20%5Cfrac%20%7Bx%20-%20y_2%7D%20%7Bx%20-%20y_1%7D%20%7D)
![\frac {d_2}{d_1} = \sqrt[4] { \frac {36.9 - 17.9} {36.9 - 8.85} }](https://tex.z-dn.net/?f=%5Cfrac%20%7Bd_2%7D%7Bd_1%7D%20%3D%20%5Csqrt%5B4%5D%20%7B%20%5Cfrac%20%7B36.9%20-%2017.9%7D%20%7B36.9%20-%208.85%7D%20%7D)



<h3>Learn more</h3>

<h3>Answer details</h3>
Grade: High School
Subject: Physics
Chapter: Kinematics