Answer:
The amount of time for the whole journey is 8 hours.
Explanation:
A truck covered 2/7 of a journey at an average speed of 40 mph. Representing 1 the total of the trip traveled, then the rest of the distance traveled is calculated as: [tex]1-\frac{2}{7} =\frac{5}{7}[/tex]
So if the truck covered the remaining 200 miles at [tex]\frac{2}{7}[/tex], this means that [tex]\frac{5}{7}[/tex] of the trip represents the 200 miles. So, to calculate the total distance traveled by the truck, you apply the following rule of three: if [tex]\frac{5}{7}[/tex] of the route represents 200 miles, the integer 1 (which represents the total of the route), how many miles are they?
[tex]miles=\frac{1*200miles}{\frac{5}{7} } =\frac{7}{5} *200 miles[/tex]
miles= 280
So the total distance traveled is 280 miles. Since speed is the relationship between the space traveled by an object and the time used for it ([tex]speed=\frac{distance}{time}[/tex]), then if the average of the entire trip was 35 mph and the distance traveled 280 miles, the time is calculated as:
[tex]time=\frac{distance}{speed}=\frac{280 miles}{35 mph}[/tex]
time= 8 h
The amount of time for the whole journey is 8 hours.
A bungee cord stretches 25 meters and has a spring constant of 140 N/m. How much energy is stored in the bungee
Answer:
87.5 kJExplanation:
The potential energy stored in a stretch spring is given by the expression below
PE = Work = force * distance
So:
[tex]PE = (kx) * x[/tex]
This then simplifies to:
[tex]PE = kx^2[/tex]
where k is the spring constant= 140 N/m
Given that x= 25 m
Substituting our data into the expression for P.E stored we have
[tex]PE = 140*25^2\\\\PE= 140*625\\\\PE= 87500 J[/tex]
Hence the energy stored in the spring is 87.5kJ
The acceleration of an object is always in the direction of the net force acting on it.
Answer:
yes
Explanation:
An object which moves in a circle is accelerating. Accelerations are caused by an unbalanced or net force. The net force is always in the same direction as the acceleration. For objects moving in circles at constant speed, the net force is directed towards the center of the circle about which the object moves.
During the class prize-giving ceremony, Anand clapped his hands hard while Kumar clapped his hands softly. Everybody could hear Anand's clapping while only a few could hear Kumar's clapping. This was because the sound produced by Anand was of____________.
A - higher pitch
B - lower frequency
C - higher volume
D- lower pitch
Answer:
C - higher volume
Explanation:
The pitch or frequency of sound that an object can produce depends upon its size and configuration . The shape of hand of all are same so the frequency of sound produced by hands of all will be almost same . Hence frequency of sound produced by the hands of Anand and Kumar would have been almost the same .
But the intensity of sound produced by them would have been different . Intensity represents energy a sound carries . Hard hitting clap will produce sound of higher intensity . Intensity of sound is also called high volume sound . So Kumar's clap will carry greater energy and hence greater volume of sound .
How many (whole number of) 87 kg people
can safely occupy an elevator that can hold a
maximum mass of exactly 1 metric ton? A
metric ton is 1.000 x 103 kg.
Answer in units of people.
Answer:
11
Explanation:
1. You are going to be rounding down.
2. change the metric ton to kg.
1.000 * 10^3 kg = 1000 kg
1000 / 87 = 11.49 = 11 people
A cellist tunes the C string of her instrument to a fundamental frequency of 65.4 Hz. The vibrating portion of the string is 0.590 m long and has a mass of 15.0 g.
(a) Calculate the wavelength corresponding to this fundamental frequency?
(b) Calculate the wave speed.
(c) With what tension must the musician stretch the string?
Answer:
a
[tex]\lambda = 1.18 \ m[/tex]
b
[tex]v = 77.172 \ m/s[/tex]
c
[tex]T = 151.41 \ N[/tex]
Explanation:
From the question we are told that
The frequency is [tex]f = 65.4 \ Hz[/tex]
The length of the vibrating string is [tex]L = 0.590 \ m[/tex]
The mass is [tex]m = 15.0 \ g = 0.015 \ kg[/tex]
Generally the wavelength is mathematically represented as
[tex]\lambda = 2 * L[/tex]
=> [tex]\lambda = 2 * 0.590[/tex]
=> [tex]\lambda = 1.18 \ m[/tex]
Generally the wave speed is
[tex]v = \lambda * f[/tex]
=> [tex]v = 1.18 * 65.4[/tex]
=> [tex]v = 77.172 \ m/s[/tex]
Generally the tension on the wire is mathematically represented as
[tex]T = v^2 * \frac{ m }{L }[/tex]
=> [tex]T = 77.172 ^2 * \frac{ 0.015 }{0.590}[/tex]
=> [tex]T = 151.41 \ N[/tex]
Unpolarized light with intensity 370W/m2 passes first through a polarizing filter with its axis vertical, then through a second polarizing filter. It emerges from the second filter with intensity 121W/m2 .
What is the angle from vertical of the axis of the second polarizing filter?
Express your answer to two significant figures and include the appropriate units
Answer:
Answer:
36°
Explanation:
Using
I= (1/2Io) cos²စ
Then Substituting
121W/m² = 1/2*370W/m²cos²စ
0.8086= cosစ
Cos^-1 0.8086= 36°
Which type of graph uses wedges to show the amount of data points in a
category?
A. Circle graph
O B. Line graph
O C. Box-and-whisker plot
D. Stemplot
The type of graph that uses wedges to show the amount of data points in a category is a Circle graph, also known as a Pie chart. In a Pie chart, the circle represents the whole data set, and each wedge represents a specific category or data point.
In a Circle graph, the entire circle represents the total amount or the whole data set being analyzed. The circle is divided into wedges or slices, with each wedge representing a specific category or data point. The size of each wedge is proportional to the amount or percentage of data points that belong to that category.
The wedges are typically labeled with the category they represent and are often accompanied by a numerical value or percentage to indicate the exact proportion of data points in that category. The labels and values help the reader interpret the graph and understand the distribution of data across different categories.
Therefore, the correct answer is A. Circle graph.
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An electron as q = 1.602 * 10-19 C is placed .03m away from spherical object with a net charge of -7.2 C.
A. What is the force exerted on the electron?
B. How strong is the electric field at the electron’s location?
C. How much work would be done on the electron if it was moved so that it’s .001m away from the sphere?
D. Now replace the electron with a positron (q = +1.602 × 10-19C). Explain.
Answer:
See explanation
Explanation:
The electric force exerted on the electron is given by Coulomb's law;
F= KqQ/r^2
F= force on the electron
K= constant of Coulomb's law
q= charge on the electron
Q=charge on the spherical object
r= distance between the charges
F= 9×10^9 × -1.602 × 10^-19 × (-7.2)/(0.03)^2
F= 103.8 × 10^-10/9×10^-4
F= 11.53 ×10^-6
F= 1.153 ×10^-5 N
The force in this case is repulsive
E= F/q
E= 1.153 ×10^-5 N/ 1.602 * 10-19 C
E= 0.719 × 10^14
E= 7.19 × 10^13 NC-1
The electro field around the electron is very strong.
c)
V= Kq/r
V= 9×10^9 × 1.602 × 10^-19/0.001
V= 14418 × 10^-10
V=1.4418 ×10^-6 V
W= qV
W= 1.602×10^-19 C × 1.4418 ×10^-6 V
W= 2.31 ×10^-25 J
Replacing the electron with a positron
F= 9×10^9 × 1.602 × 10^-19 × (-7.2)/(0.03)^2
F= 103.8 × 10^-10/9×10^-4
F= 11.53 ×10^-6
F= -1.153 ×10^-5 N
The force in this case is attractive
Moving mirror M2 of a Michelson interferometer a distance of 90 μm causes 470 bright-dark-bright fringe shifts.What is the wavelength of the light?
Answer:
Wavelength, [tex]\lambda=382.9\ nm[/tex]
Explanation:
It is given that,
Distance moved by mirror in Michelson interferometer is 90 μm
Number of bright fringe shift = 470
We need to find the wavelength of the light.
For Michelson interferometer experiment,
[tex]2d=m\lambda[/tex]
here, [tex]\lambda[/tex] is the wavelength of the light
[tex]\lambda=\dfrac{2d}{m}\\\\\lambda=\dfrac{2\times 90\times 10^{-6}}{470}\\\\\lambda=3.829\times 10^{-7}\ m\\\\\lambda=382.9\ nm[/tex]
So, the wavelength of the light is 382.9 nm.
The wavelength of the light should be 382.9nm.
Calculation of the wavelength of the light:Since
Distance moved by the mirror in Michelson interferometer is 90 μm
And, Number of bright fringe shift = 470
So
we know that
2d = m*wavelength
wavelength = 2*90*10^-6/470
= 3.829*10^-7m
= 382.9nm
hence, The wavelength of the light should be 382.9nm.
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While the block hovers in place, is the density of the block (top left) or the density of the liquid (bottom center) greater?
Answer:
for the body to float, the density of the body must be less than or equal to the density of the liquid.
Explanation:
For a block to float in a liquid, the thrust of the liquid must be greater than or equal to the weight of the block.
Weight is
W = mg
let's use the concept of density
ρ_body = m / V
m = ρ_body V
W = ρ_body V g
The thrust of the body is given by Archimedes' law
B = ρ_liquid g V_liquid
as the body floats the submerged volume of the liquid is less than or equal to the volume of the block
ρ_body V g = ρ_liquid g V_liquid
ρ_body = ρ liquid Vliquido / V_body
As we can see, for the body to float, the density of the body must be less than or equal to the density of the liquid.
With the LED illuminated, flip the direction of the LED on the breadboard (notch on top now), and then flip it back to its original position (notch on bottom). What does your observation tell you about diodes (and LEDs)?
Explanation:
The full form of LED is Light Emitting Diode. It is a semi conductor source of light which when electrons passes or flows through them, it emits light. In the semi conductor, the electrons recombine with the electron holes to release high amount of energy. This energy is called photon.
When the LED direction is flipped in the breadboard and back to the original position, the LEDs are forced to be grounded. They will not be able to function without being grounded.
In what way is the study of psychology similar to other “hard sciences”? A. use of the scientific method B. use of memory C. use of emotion D. use of behavior
Answer:
The correct option is a
Explanation:
Psychology can be defined as the "scientific study" of the mind and behavior of humans and other animals. It involves the use of scientific methods in determining or understanding the social, physiological and biological behaviors in different groups or individual organisms
The correct option is a
The following information should be considered:
Psychology refers to the "scientific study" of the mind & behavior of humans and other animals. It includes the use of scientific methods in measurement or understanding the social, physiological ,and biological behaviors in different groups or individual organisms.Learn more: https://brainly.com/question/17429689?referrer=searchResults
A helicopter blade spins at exactly 180 revolutions per minute. Its tip is 10.00 m from the center of rotation. What is its average velocity over one revolution
Answer:
5.8E-3m/s
Explanation:
Using
V= d/t
V= velocity
d= distance
t= time
But d= 2πr
But 180rev= 1min
So 1min/180= 60s/180
So
Vavr= 2π(10m)/180*60
=5.8E-3m/s
Cousin Throckmorton is playing with the clothesline. One end of the clothesline is attached to a vertical post. Throcky holds the other end loosely in his hand, so that the speed of waves on the clothesline is a relatively slow 0.700 m/s . He finds several frequencies at which he can oscillate his end of the clothesline so that a light clothespin 40.0 cm from the post doesn't move. What are these frequencies?
Answer:
The frequencies are [tex]f_n = n (0.875 )[/tex]
Explanation:
From the question we are told that
The speed of the wave is [tex]v = 0.700 \ m/s[/tex]
The length of vibrating clothesline is [tex]L = 40.0 \ cm = 0.4 \ m[/tex]
Generally the fundamental frequency is mathematically represented as
[tex]f = \frac{v}{2 L }[/tex]
=> [tex]f = \frac{ 0.700 }{2 * 0.4 }[/tex]
=> [tex]f = 0.875 \ Hz[/tex]
Now this other frequencies of vibration experience by the clotheslines are know as harmonics and they are obtained by integer multiple of the fundamental frequency
So
The frequencies are mathematically represented as
[tex]f_n = n * f[/tex]
=> [tex]f_n = n (0.875 )[/tex]
Where n = 1, 2, 3 ....
Two lasers are shining on a double slit, with slit separation d. Laser 1 has a wavelength of d/20, whereas laser 2 has a wavelength of d/15. The lasers produce separate interference patterns on a screen a distance 6.00 m away from the slits.
Which laser has its first maximum closer to the central maximum?
What is the distance Image for Two lasers are shining on a double slit, with slit separation d. Laser 1 has a wavelength of d/20, whereas las between the first maxima (on the same side of the central maximum) of the two patterns?
Two lasers are shining on a double slit, with slit separation d. Laser 1 has a wavelength of d/20, whereas las= ______ m
What is the distance Deltay_max-min between the second maximum of laser 1 and the third minimum of laser 2, on the same side of the central maximum?
Deltay_max-min = ______ m
Answer:
A) Therefore laser1 has the maximum closest to the central maximum
B) Δₓ = 0.8
Explanation:
A) The expression for the constructive interference of a double slit is
d sin θ = m λ
let's use trigonometry to find the angle
tan θ = y / L
in interference phenomena the angles are small
tan θ = sin θ / cos θ = sin θ
sin θ = y / L
we subjugate
d y / L = m λ
y = m λ L / d
let's apply this equation for each case
a) Lares 1 has a wavelength λ₁ = d / 20, the screen is at L = 6.00 m
they ask us for the first axiom m = 1,
let's calculate
y₁ = 1 (d / 20) 6.00 / d
y₁ = 0.3
Laser 2, λ₂ = d / 15
λ₂ = 1 (d / 15) 6.00 / d
λ₂ = 0.4
Therefore laser1 has the maximum closest to the central maximum
b) let's find the distance of each requested value
second maximum m = 2 of laser 1
yi '= 2 (d / 20) 6 / d
y1 '= 0.6
3rd minimum of laser 2
the expression for destructive interference is
d sinθ = (m + 1/2) lam
y = (m ) λ L / d
in this case m = 3
let's calculate
y2 '= (3+0.5) (d / 15) 6 / d
y2 '=21/15
They ask us for the dalt of these interference
Δₓ = y3 -y2'
Δₓ = 21/15 - 0.6
Δₓ = 0.8
A remote-controlled toy car travels at a constant speed of 3 m/s. What distance does the car travel in 6 seconds?
Answer:
speed=d/t.
3=d/6.
d=3×6=18m
A standard gold bar stored at Fort Knox, Kentucky, is 7.00 inches long, 3.63 inches wide, and 1.75 inches tall. Gold has a density of 19,300 kg/m3. What is the mass of such a gold bar?
Answer:
14.1 kg
Explanation:
Given:
Length=7.00inches
Width=3.63 inches
Height=1.75 inches
density = 19,300 kg/m3.
We can convert the given parameters to metre for unit consistency
But we know 1 inches= 0.0254 metre
✓Then Length l=7.00inches
=7×0.0254 metre=0.1778m
✓Width w =3.63 inches
==3.63 ×0.0254 metre=0.092m
✓Height h =1.75 inches
=1.75 ×0.0254 metre=0.0445 m
But Mass= density × volume
Volume= Length× width×height
Mass= density× Length× width×height
= 19300kg/m³×0.1778×0.0922×0.0445
=14.1 kg
Therefore, the mass of the gold bar is 14.1 kg
The mass of such a gold bar is of 13.89 kg.
Given data:
The length of gold bar is, [tex]L=7.00 \;\rm in =7.00 \times 0.0254=0.1778 \;\rm m[/tex].
The width of gold bar is, [tex]w= 3.63 \;\rm in =3.63 \times 0.0254 = 0.092 \;\rm m[/tex].
The height if gold bar is, [tex]h = 1.75 \;\rm in =0.044 \;\rm m[/tex].
The density of the gold bar is, [tex]\rho =19,300 \;\rm kg/m^{3}[/tex].
The given problem is based on the concept of density. The density of any substance is equal to the ratio of mass and volume. Considering the gold bar to rectangular shape, the volume of gold bar is calculated as,
[tex]V= L \times w \times h\\\\V = 0.1778 \times 0.092 \times 0.044\\\\V=7.197 \times 10^{-4} \;\rm m^{3}[/tex]
Now, use the formula of density to calculate the mass of gold bar as,
[tex]\rho =\dfrac{m}{V}\\\\m = \rho \times V\\\\m = 19300 \times (7.197 \times 10^{-4})\\\\m= 13.89 \;\rm kg[/tex]
Thus, we can conclude that the mass of such a gold bar is of 13.89 kg.
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You are looking down on a N = 17 turn coil in a magnetic field B = 0.5 T which points directly down into the screen. If the diameter of the coil d = 3.8 cm, and the field goes to zero in t = 0.24 seconds, what would be the magnitude of the voltage (in Volts) and direction of the induced current? Indicate the direction of the current by the sign in front of your voltage: counterclockwise is positive, clockwise is negative.
Complete Question
The diagram for this question is shown on the first uploaded image
Answer:
The voltage is [tex]\epsilon = 0.40163 \ V[/tex]
The direction of the induced current is clockwise
Explanation:
From the question we are told that
The number of turns is N = 17
The magnetic field is [tex]B_2 = 0.5 \ T[/tex]
The diameter is [tex]d = 3.8 \ cm = 0.038 \ m[/tex]
The time interval is [tex]dt = 0.24 \ s[/tex]
The induce emf is mathematically represented as
[tex]\epsilon = - N \frac{d\phi}{dt}[/tex]
[tex]\epsilon = - N \frac{d ( B_2 - B_1 ) A }{dt}[/tex]
Here [tex]B_1[/tex] is the magnetic field experienced by the coil before entering the magnetic field given in the question i.e [tex]B_1 = 0[/tex]
Here the negative sign show that the induced voltage is moving in a direction opposite to the change magnetic flux
The area is mathematically represented as
[tex]A = \pi \frac{d^2}{4}[/tex]
=> [tex]A = 3.142 * \frac{ 0.038^2 }{4}[/tex]
=> [tex]A = 0.01134 \ m^2[/tex]
Hence
[tex]\epsilon = - 17 * \frac{ 0.5 * 0.01134 }{ 0.24}[/tex]
[tex]\epsilon = 0.40163 \ V[/tex]
The direction of the induced current is the same as that of induced voltage
Thus the direction is clockwise
An object is moving with constant non-zero velocity. Which of the following statements about it must be true?
(A) A constant force is being applied to it in the direction of motion.
(B) A constant force is being applied to it in the direction opposite of motion.
(C) A constant force is being applied to it perpendicular to the direction of motion.
(D) The net force on the object is zero.
(E) Its acceleration is in the same direction as its velocity.
Answer:
The net force on the object is zero.
Explanation:
An object is moving with constant non-zero velocity. If velocity is constant, it means that the change in velocity is equal to 0. As a result, acceleration of the object is equal to 0. Net force is the product of mass and acceleration. Hence, the correct option is (d) "The net force on the object is zero".
For a constant non-zero velocity the net force on the object is zero.
Velocity is defined as the change in displacement per change in time of motion.
[tex]v = \frac{\Delta x}{\Delta t}= \frac{x_2 - x_1}{t_2 - t_1}[/tex]
where;
Δx is the change in displacement
Δt is the change in time motion
When the change in the displacement is same for equal time interval, the resulting velocity will be constant but non-zero in magnitude.
Also, when the net force acting on an object is zero, the object will move with a constant velocity.
[tex]\Sigma F_x = 0[/tex]
Thus, for a constant non-zero velocity the net force on the object is zero.
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A 26.5-mW laser beam of diameter 1.88 mm is reflected at normal incidence by a perfectly reflecting mirror. Calculate the radiation pressure on the mirror.
Answer:
Explanation:
Area= pier^2
=( 1.88/2)^2= 0.0000000314m^2
Intensity= 0.0265/0.000000314
= 7962W/m^2
Pressure= 2*7962)/345= 5.13*10^-5pa
: The maximum theoretical efficiency of a Carnot engine operating between reservoirs at the steam point and at room temperature is about A :
Answer:
The value is [tex]\eta = 0.2145[/tex] or 21.45%
Explanation:
From the question we are told that
The first reservoir is at steam point [tex]T_s = 100^o C = 100 + 273 = 373 \ K[/tex]
The second reservoir is at room temperature [tex]T_r = 20^o C = 293 \ K[/tex]
Generally the maximum theoretical efficiency of a Carnot engine is mathematically evaluated as
[tex]\eta = 1- \frac{T_r}{T_s}[/tex]
=> [tex]1 - \frac{ 293}{373}[/tex]
=> [tex]\eta = 0.2145[/tex]
A series RLC circuit connected across an ac voltage source has minimum current flowing through the circuit when operating at the resonant frequency. is this statement true or false and why?
Answer:
False
Explanation:
This is because Since the current flowing through a series resonance circuit is the product of voltage divided by impedance, at resonance the impedance, Z is at its minimum value, ( =R ). So, the circuit current at this frequency will be at its maximum value of V/R
A small loop of area 8.8 mm² is placed inside a long solenoid that has 818 turns/cm and carries a sinusoidally varying current i of amplitude 1.28 A and angular frequency 212 rad/s. The central axes of the loop and solenoid coincide.What is the amplitude of the emf induced in the loop?
Answer:
The amplitude of the induced emf is [tex]\epsilon_a = 2.45*10^{-4}\ V[/tex]
Explanation:
From the question we are told that
The area is [tex]A = 8.8 \ mm^2 = 8.8 *10^{-6} \ m[/tex]
The number f turns per cm is [tex]N = 818 \ turn/cm = 81800 \ turn /m[/tex]
The current is [tex]I = 1.28 \ A[/tex]
The angular frequency is [tex]w = 212 \ rad /s[/tex]
Generally the amplitude of the induced emf is mathematically represented as
[tex]\epsilon_a = \mu_o * N * I * w * A[/tex]
Where [tex]\mu_o[/tex] is the permeability of free space with value [tex]\mu_o = 4\pi * 10^{-7} N/A^2[/tex]
=> [tex]\epsilon_a = 4\pi * 10^{-7} * 81800 * 1.28 * 212 * 8.8*10^{-6}[/tex]
[tex]\epsilon_a = 2.45*10^{-4}\ V[/tex]
So we were working on some pulley problems but this one has kinda left me scratching my head, please help! My question is for part C :' )
Explanation:
(c) I assume we're looking for mA.
Sum of forces on B in the -y direction:
∑F = ma
mBg − T = mBa
Sum of forces on A in the +x direction:
∑F = ma
T = mAa
Substitute:
mBg − mAa = mBa
mBg − mBa = mAa
mA = mB (g − a) / a
Plug in values:
mA = (5 kg) (10 m/s² − 0.01 (10 m/s²)) / (0.01 (10 m/s²))
mA = 495 kg
The answer key seems to have a mistake. It's possible they meant mB = 1 kg, or they changed mB to 5 kg but forgot to change the answer.
Imagine you derive the following expression by analyzing the physics of a particular system: M= (mv2r)(mGr2). Simplify the expression for M using the techniques mentioned above.
Answer:
The simplified expression is [tex]M = \frac{v^2 r}{G}[/tex]
Explanation:
From the question we are told that
[tex]M = \frac{ \frac{m v^2}{r} }{\frac{ mG}{r^2 } }[/tex]
So simplifying we have
[tex]M = \frac{m v^2}{r} * \frac{r^2 }{ mG }[/tex]
[tex]M = \frac{v^2 r}{G}[/tex]
Thus the simplified formula is [tex]M = \frac{v^2 r}{G}[/tex]
the kinetic energy of a body executing simple harmonic motion of amplitude A is equal to the potential energy when its displacement is
Answer:
My answer to the question is "when its displacement is zero.
A boy weighing 70 kg is standing on the sand. Calculate the pressure on if you are resting on your feet, whose surfaces add up to 0.035 m2 and if you are resting on diving fins of 0.300 × 0.42 m each
Explanation:
Pressure = force / area
If you are standing on your feet:
P = (70 kg × 10 m/s²) / (0.035 m²)
P = 20,000 Pa
If you are standing on diving fins:
P = (70 kg × 10 m/s²) / (2 × 0.30 m × 0.42 m)
P ≈ 2,800 Pa
What is charging by contact
Answer:
Charging by contact is when the charged object is brought near but never contacted to the object being charged
Explanation:
a burning piece of wood converts ____ energy into ____ energy
Answer:
a burning piece of converts Chemical energy into Heat(Thermal) and Light energy
A superball has a coefficient of restitution of .90. The ball is dropped from an intitial height of 1.60m.
a) if the ball is allowed to bounce 3 times, how high will it rebound after the third bounce?
b) If the ball has a mass of 48g, calculate the amount of the ball's orignal energy that was lost in the three impacts with the floor.
Answer:
a
[tex]H_3 = 0.85 \ m[/tex]
b
[tex]PE = 0.3528 \ J[/tex]
Explanation:
From the question we are told that
The coefficient of resolution is [tex]C_r = 0.90[/tex]
The initial height is [tex]H_i = 1.60 \ m[/tex]
Considering question a
The number of times the ball bounced is [tex]k = 3[/tex]
Generally the height attained after the 3rd bounce is mathematically represented as
[tex]H_3 = H_i * (C_r)^{2 * k }[/tex]
=> [tex]H_3 = 1.60 * 0.90^{2 * 3 }[/tex]
=> [tex]H_3 = 0.85 \ m[/tex]
Considering question b
The mass is m = 48 g = 0.048 kg
Generally the amount of potential energy that was lost is mathematically represented as
[tex]PE = mg [ H_i - H_3 ][/tex]
=> [tex]PE = 0.048 * 9.8 [1.60 - 0.85 ][/tex]
=> [tex]PE = 0.3528 \ J[/tex]