The pH electrode is in the solution where the pH is measured and connected to the pH meter which has a readout. It takes one kin
1 answer:
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In order to solve this problem, there are two equations that you need to know to solve this problem and pretty much all of kinematics. The first is that d=0.5at^2 (d=vertical distance, a=acceleration due to gravity and t=time). The second is vf-vi=at (vf=final velocity, vi=initial velocity, a=acceleration due to gravity, t=time). So to find the time that the ball traveled, isolate the t-variable from the d=0.5at^2. Isolate the t and the equation now becomes 
. Solving the equation where d=8 and a=9.8 makes the time 
=1.355 seconds. With the second equation, the vi=0 m/s, the vf is unknown, a=9.8 m/s^2 and t=1.355 sec. Substitute all these values into the equation vf-vi=at, this makes it vf-0=9.8(1.355). This means that the vf=13.28 m/s.
Answers:
a)
b)
Explanation:
This situation is a good example of the projectile motion or parabolic motion, in which the travel of the snowball has two components: <u>x-component</u> and <u>y-component</u>. Being their main equations as follows for both snowballs:
<h3><u>Snowball 1:</u></h3><u>x-component: </u>
(1)
Where:
is the initial speed of snowball 1 (and snowball 2, as well)
is the angle for snowball 1
is the time since the snowball 1 is thrown until it hits the opponent
<u>y-component: </u>
(2)
Where:
is the initial height of the snowball 1 (assuming that both people are only on the x axis of the frame of reference, therefore the value of the position in the y-component is zero.)
is the final height of the snowball 1
is the acceleration due gravity (always directed downwards)
<u>x-component: </u>
(3)
Where:
is the angle for snowball 2
is the time since the snowball 2 is thrown until it hits the opponent
<u>y-component: </u>
(4)
Having this clear, let's begin with the answers:
<h2>a) Angle for snowball 2</h2>Firstly, we have to isolate from (2):
(5)
(6)
Substituting (6) in (1):
(7)
Rewritting (7) and knowing :
(8)
(9)
(10) This is the point at which snowball 1 hits and snowball 2 should hit, too.
With this in mind, we have to isolate from (4) and substitute it on (3):
(11)
(12)
Rewritting (12):
(13)
Finding :
(14)
(15) This is the second angle at which snowball 2 must be thrown. Note this angle is lower than the first angle
.
<h2>b) Time difference between both snowballs</h2>
Now we will find the value of and
from (6) and (11), respectively:
(16)
(17)
(18)
(19)
Since snowball 1 was thrown before snowball 2, we have:
(20)
Finding the time difference between both:
(21)
Finally: