(a) The ball's height <em>y</em> at time <em>t</em> is given by
<em>y</em> = (20 m/s) sin(40º) <em>t</em> - 1/2 <em>g t</em> ²
where <em>g</em> = 9.80 m/s² is the magnitude of the acceleration due to gravity. Solve <em>y</em> = 0 for <em>t</em> :
0 = (20 m/s) sin(40º) <em>t</em> - 1/2 <em>g t</em> ²
0 = <em>t</em> ((20 m/s) sin(40º) - 1/2 <em>g t</em> )
<em>t</em> = 0 or (20 m/s) sin(40º) - 1/2 <em>g t</em> = 0
The first time refers to where the ball is initially launched, so we omit that solution.
(20 m/s) sin(40º) = 1/2 <em>g t</em>
<em>t</em> = (40 m/s) sin(40º) / <em>g</em>
<em>t</em> ≈ 2.6 s
(b) At its maximum height, the ball has zero vertical velocity. In the vertical direction, the ball is in free fall and only subject to the downward acceleration <em>g</em>. So
0² - ((20 m/s) sin(40º))² = 2 (-<em>g</em>) <em>y</em>
where <em>y</em> in this equation refers to the maximum height of the ball. Solve for <em>y</em> :
<em>y</em> = ((20 m/s) sin(40º))² / (2<em>g</em>)
<em>y</em> ≈ 8.4 m
The period will be the same if the amplitude of the motion is increased to 2a
What is an Amplitude?
Amplitude refers to the maximum extent of a vibration or oscillation, measured from the position of equilibrium.
Here,
mass m is attached to the spring.
mass attached = m
time period = t
We know that,
The time period for the spring is calculated with the equation:
Where k is the spring constant
Now if the amplitude is doubled, it means that the distance from the equilibrium position to the displacement is doubled.
From the equation, we can say,
Time period of the spring is independent of the amplitude.
Hence,
Increasing the amplitude does not affect the period of the mass and spring system.
Learn more about time period here:
<u>brainly.com/question/13834772</u>
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Answer:
Their function is to produce sound by allowing the free edges of the folds to vibrate against one another and also to act as the laryngeal sphincter when they are closed.
Complete Question
A parallel-plate capacitor, with air dielectric, is charged by a battery, after which the battery is disconnected. A slab of glass dielectric is then slowly inserted between the plates. As it is being inserted,
A :
a force repels the glass out of the capacitor.
B :
a force attracts the glass into the capacitor.
C :
no force acts on the glass.
D :
a net charge appears on the glass.
E :
the glass makes the plates repel each other.
Answer:
The correct option is B
Explanation:
Generally when the glass dielectric is slowly inserted between the plated,
The positive plate of the capacitor will induce a negative charge on the glass while the negative plate of the capacitor will induce a positive charge on glass which a electric field that posses an electric force that will attract the glass
Answer:
True
Explanation:
Given that Power whose unit is Watt equates to one joule of work per second. It implies that Power is directly proportional to the work done and inversely proportional to the time to do the work.
Therefore, in this case, the right answer to the question is that it is TRUE that the power is inversely proportional with time
