Answer: 2 hr 45 min
Explanation:
Given
The average speed between San Diego and Los Angeles is
time taken for this trip is
Distance between San Diego and Los Angeles is
For Friday afternoon, the average speed is
time taken to complete the trip is
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:
Explanation:
Let f₁ is the fundamental frequency,
Lower pitch frequency,
Fundamental frequency is, .....(1)
Lower frequency is, ..............(2)
Dividing equation (1) and (2) as :
So, the ratio of linear mass density μ of the string with the higher pitch to that of the string with the lower pitch is 0.00132. Hence, this is the required solution.