Given that,
The equation is "F=kx"
To find,
The derivative equation.
Solution,
We are given with the given equation which is as follows :
F = kx ...(1)
Where, F is force, k is spring constant and x is distance covered by the spring
Differentiate equation (1) wrt x.
[tex]\dfrac{dF}{dx}=\dfrac{d}{dx}(kx)\\\\\dfrac{dF}{dx}=k[/tex]
As k is constant.
Hence, this is the required solution.
A sky diver is falling through air, and the forces on him are air resistance 1400 N upward and gravity 2200 N downward. What is the magnitude of the net force acting on him?
329 N
800 N
3200 N
11,760 N
What is the mass of the skydiver?
91.6 kg
120 kg
210 kg
224.5 kg
What is the acceleration of him?
3.56 m/s2
5.3 m/s2
15.7 m/s2
35.6 m/s2
Answer:
Fresultant = - 800 [N]
m = 224.26 [kg]
a = 3.56 [m/s²]
Explanation:
The resulting force can be determined by the arithmetic difference of the air resistance force and the gravity force.
[tex]F_{resultant}=F_{air}-F_{gravity}\\F_{resultant}=1400-2200\\F_{resultant}=-800[N][/tex]
The negative sign of the result means that the force is directed downwards.
The mass can be easily calculated using the definition of the weight of the body. Where the weight is equal to the product of mass by gravitational acceleration.
[tex]W =m*g\\[/tex]
where:
m = mass [kg]
W = weight = 2200 [N]
g = gravity acceleration = 9.81 [m/s²]
[tex]m=W/g\\m=2200/9.81\\m= 224.26 [kg][/tex]
Finally, acceleration can be calculated using Newton's second law which tells us that the resulting force on a body is equal to the product of mass by acceleration.
[tex]F_{resultant}=m*a\\-800 = - 224.26*a\\a=3.56 [m/s^{2} ]\\[/tex]
The positive sign of acceleration tells us that effectively the body moves down.
Newton's 2nd Law describes the relationship between force, mass, and acceleration of an object with the formula F=ma. Which scenario below will result in the greatest accleration? (AKS 8b / DOK 1)
A. A 20 kg rock thrown with a 100 N force.
B. A 10,000 kg rocket launched with 100,000 N of force.
C. A 2,000 kg car accelerated with a 1000 N force from the engine.
D. A 50 kg student pushed in a chair with a force of 1000 N.
Answer:D
Explanation:If you want to find the acceleration do Force/mass.
The greatest magnitude of acceleration is of 20 m/s², by the student of 50 kg pushing the chair with 1000 N of force. Hence, option (D) is correct.
As per the Newton's second law, " The applied force on an object is equal to the product of mass of object and acceleration cause by the applied force. Then, the mathematical expression is,
F = ma
Here, F is the applied force, m is the mass and a is acceleration.
(A)
For 20 kg mass and 100 N force, the acceleration is,
F = ma
100 = (20)a
a = 5 m/s²
(B)
For 10,000 kg mass of rocket and 100,000 N force, the acceleration is,
F = ma
100 ,000= (10,000)a
a = 10 m/s²
(C) For a 2,000 kg mass of car and force of 1000 N, the acceleration is,
F = ma
1000 = (2000)a
a = 0.5 m/s²
(D) For a mass of 50 kg student and applied force of 1000 N, the acceleration is,
F = ma
1000 = (50)a
a =20 m/s².
Thus, we can conclude that the greatest magnitude of acceleration is of 20 m/s², by the student of 50 kg pushing the chair with 1000 N of force. Hence, option (D) is correct.
Learn more about the Newton's Second law here:
https://brainly.com/question/13447525
3. Two balls are rolling toward each other. One has a momentum of 85kg*m/s, and the other has a momentum of -85kg*m/s. What will be the total momentum of the system after they collide? In what direction will they move after they collide if it is an inelastic collision? Answer:
Answer:
The total momentum is zero.
Explanation:
This problem can be solved by applying the momentum conservation theorem and the amount of motion. This theorem tells us that the amount of motion is conserved before and after a collision.
In the next equation, we will write to the left of the equal sign the amount of motion before the collision and to the right the amount of motion after the collision.
[tex](P_{1})-(P_{2})=P_{3}[/tex]
where:
P₁ = momentum of the ball moving to the right, before the collision = 85 [kg*m/s]
P₂ = momentum of the ball moving to the left, before the collision = - 85 [kg*m/s]
P₃ = Final momentum after the collision [kg*m/s]
[tex](85) - 85 = P_{3}\\P_{3}= 0[/tex]
There is no movement of any of the balls, they remain at rest after the impact.
How long does it take to accelerate from 8.0 m/s to 20.0 m/s at a rate of acceleration of 3.0 m/s2?
Question 17 options:
4.0 s
0.25 s
36 s
9.33 s
Answer:
4.0s
Explanation:
v = v_0 + a*t -> t = (v - v_0) / a
v = 20.0m/s, v_0 = 8.0 m/s, a = 3.0 m/s^2
t = (20.0 - 8.0) / 3.0 = 4.0s
Answer:
t = 4.0 s
Explanation:
Given:
V₁ = 8.0 m/s
V₂ = 20.0 m/s
a =3.0 m/c²
______________
t - ?
a = ( V₂ - V₁ ) / t
t = ( V₂ - V₁ ) / a
t = ( 20.0 - 8.0 )/ 3.0 = 12.0 /3.0 = 4.0 s
A nearsighted person has a far point of 40cm. What power spectacle lens is needed if the lens is 2cm from the eye
Answer:
The value is [tex]p = - 2.63 \ Diopters[/tex]
Explanation:
From the question we are told that
The value of the far point is [tex]a = 40 \ cm = 0.4 \ m[/tex]
The distance of the lens to the eye is [tex]b = 2 \ cm = 0.02[/tex]
Generally
[tex]1 Diopter = > 1 m^{-1}[/tex]
Generally the power spectacle lens needed is mathematically represented as
[tex]p = \frac{1}{d_o } + \frac{1}{d_i}[/tex]
Here [tex]d_o[/tex] is the object distance which for a near sighted person is [tex]d_o = \infty[/tex]
And [tex]d_i[/tex] is the image distance which is evaluated as
[tex]d_i = b - a[/tex]
=> [tex]d_i = 0.02 - 0.4[/tex]
=> [tex]d_i = -0.38 \ m[/tex]
So
[tex]p = \frac{1}{\infty } + \frac{1}{-0.38}[/tex]
=> [tex]p = 0 - 2.63[/tex]
=> [tex]p = - 2.63 \ Diopters[/tex]
The energy of microwaves is less than the energy of ultraviolet light. Which comparison of the energies of
electromagnetic waves is correct?
O Gamma rays have higher energy than microwaves because gamma rays have shorter wavelengths.
O Gamma rays have higher energy than microwaves because gamma rays have lower frequencies.
O Infrared light has lower energy than X-rays because infrared light has shorter wavelengths.
O Infrared light has lower energy than X-rays because infrared light has higher frequencies.
Answer:
A. Gamma rays have higher energy than microwaves because gamma rays have shorter wavelengths.
Explanation:
Electromagnetic waves are waves produced by the interaction between both magnetic and electric fields. These waves have some properties that make them to be arranged in a definite form producing an electromagnetic spectrum.
The spectrum has a general property of which as the wavelength of the waves increases, the frequency decreases. And vice versa.
Thus, the energy of the waves increases as the frequency increases.
Gamma rays have higher frequency, but shorter wavelength. While microwaves has lower frequency, but higher wavelength.
Answer:
Yes, the answer is A
Explanation:
PLS HELP. What is the result of two waves meeting each other?
A. diffraction
B. reflection
C. refraction
D. interference
Answer:
D- Interference
Explanation:
When two waves meet they interfere with one another resulting in Interference
If earth squeezed to the size of moon.Calculate the weight of 100kg mass in the squeezed earth.
Answer:
833.9kg that's the answer
If the radius of a sphere increases by a factor of 2.50, by what factor does the volume of the sphere change?
Answer:
.................
Explanation:
....
...............
What does human ethics mean?
Get a little long
Thanks
Explanation:
Ethics, also called moral philosophy, the discipline concerned with what is morally good and bad and morally right and wrong. The term is also applied to any system or theory of moral values or principles. Its subject consists of the fundamental issues of practical decision making, and its major concerns include the nature of ultimate value and the standards by which human actions can be judged right or wrong.
hope it helps!
A diver 50 m deep in 10∘C fresh water exhales a 1.0-cm-diameter bubble. What is the bubble's diameter just as it reaches the surface of the lake, where the water temperature is 20∘C?
Answer:
18.2mm
Explanation:
D = 50m
T1 = 10+273 = 283K
T2 = 20+273 = 293K
R1 = 5x10^-3
Absolute pressure at 50m
P1 = pA + pwateer x g x d
= 101000+ 1000x9.81x50
= 591500pa
New volume of bubble
= P1v1/T1 = p2v2/T2
= 125x10^-9 x 591500x293/101000*283
= 757.9x10^-9m³
R2 = 9.2x10^-3
D2 = 18.2mm
Or 1.82cm
Which element is usually listed first in the formula of a binary
molecular compound
a the element with the smallest atomic radius
b the element with the lowest electronegativity
C the element with the smallest atomic mass
d the element that is first in alphabetical order help!
Answer: the element with the lowest electronegativity
Explanation:
A 0.5 kg ball was kicked and was going 15 m/s.What is the kinetic energy of the ball?
Answer:
[tex]\boxed {\boxed {\sf 56.25 \ Joules}}[/tex]
Explanation:
Kinetic energy can be found using the following formula:
[tex]E_k=\frac{1}{2}mv^2[/tex]
where m is the mass and v is the velocity.
The mass of the ball is 0.5 kilograms and the velocity is 15 meters per second
[tex]m= 0.5 \ kg \\v= 15 \ m/s \\[/tex]
Substitute the values into the formula.
[tex]E_k=\frac{1}{2} (0.5 \ kg ) * (15 \ m/s)^2[/tex]
First, evaluate the exponent.
(15 m/s)²= (15 m/s) * (15 m/s) = 225 m²/s²[tex]E_k=\frac{1}{2} (0.5 \ kg ) *(225 \ m^2/s^2)[/tex]
Multiply 0.5 kg by 225 m²/s²
[tex]E_k=\frac{1}{2}(112.5 \ kg* m^2/s^2)[/tex]
Multiply 112 kg*m²/s² by 1/2, or divide by 2.
[tex]E_k=56.25 \ kg*m^2/s^2[/tex]
1 kg*m²/s² is equal to 1 JouleTherefore, our answer of 56.25 kg*m²/s² is equal to 56.25 Joules.[tex]E_k= 56.25 \ J[/tex]
The kinetic energy of the ball is 56.25 Joules
define electric potential at a point and find expression for it.
Answer:
Recall that the electric potential is defined as the potential energy per unit charge, i.e. V=PEq V = PE q . ... The equation for the electric potential due to a point charge is V=kQr V = kQ r , where k is a constant equal to 9.0×109 N⋅m2/C2.
Explanation:
A 30 kg table is pushed forward with a force of 12 N. Friction pushes back with a
force of 5 N. What is the net force?!!
Answer:
a = 0.23 [m/s²]
Explanation:
To solve this problem we must use Newton's second law, which tells us that the sum of forces on a body is equal to the product of mass by acceleration.
∑F = m*a
where:
F = forces applied [N]
m = mass = 30 [kg]
a = acceleration [m/s²]
Now we can use Newton's second law, with forces pointing to the right as positives and negative forces pointing towards the left.
[tex]12 - 5 = 30*a\\7 = 30*a\\a = 0.23 [m/s^{2} ][/tex]
Exponential population growth is a major issue that threatens the stability of on Earth. Which of the following is not a factor used to measure human population growth for a given country?
a pendulum oscillates 25 times in 5 seconds calculate itrs time period and frequency
Answer:
I. Time period = 0.2 seconds.
II. Frequency = 5 Hertz.
Explanation:
Given the following data;
Time, t = 5 seconds.
Number of oscillation, n = 25 times
I. To find the time period;
[tex] Time \; period = \frac {time}{number \; of \; oscillations}[/tex]
Substituting into the equation, we have;
[tex] Time \; period = \frac {5}{25}[/tex]
Time period = 0.2 seconds.
II. To find frequency;
[tex] Frequency = \frac {1}{Time \; period}[/tex]
Substituting into the equation, we have;
[tex] Frequency = \frac {1}{0.2}[/tex]
Frequency = 5 Hertz.
Therefore, the time period and frequency of the pendulum is 0.2 seconds and 5 Hertz respectively.
Given the data in the question;
Number of oscillation in time t; [tex]n = 25[/tex]
Time taken for the oscillation; [tex]t = 5s[/tex]
Time period
Using the expression for Time period:
[tex]Time \ period = \frac{t}{Number\ of\ oscillation}[/tex]
We substitute our given value into the equation
[tex]Time \ period = \frac{5s}{25}\\\\Time \ period = 0.2s[/tex]
Hence, the time period is 0.2 seconds
Also, using the formula for frequency:
[tex]f = \frac{1}{T}[/tex]
Where f is frequency and T is time period.
We substitute our values into the equation
[tex]f = \frac{1}{0.2s} \\\\f = 5s^{-1}\\\\f = 5Hz[/tex]
Therefore, the frequency of the pendulum is 5 Hertz.
Learn more: https://brainly.com/question/24159297
A truck is moving north word at a constant speed the momentum of the car is
Answer:
its constant i think
Explanation:
or its stable dunno which term will they be using
When a truck is moving north word having mass 2000kg at a constant speed of 50m/s the momentum of the truck is 100000 kg.m/s.
What is Momentum ?Momentum is defined as product of mass and velocity of the body. It is denoted by letter p and it is expressed in kg.m/s.
Mathematically p = mv. it discuss the moment of the body. body having zero mass or velocity has zero momentum.
The dimensions of the momentum is [M¹ L¹ T⁻¹].
In this problem velocity and mass of the truck is not given, Consider the mass of the truck is 2000kg and speed is 50m/s.
Given,
m = 2000kg
v = 50m/s
The momentum p = mv = 2000×50 =100000 kg.m/s
To know more about momentum :
https://brainly.com/question/30677308
#SPJ2.
A river flows due east at 1.50 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10 m/s due north relative to the water.(a) What is the velocity of the boat relative to the shore?(b) If the river is 300 m wide, how far downstream has the boat moved by the time it reaches the north shore?
Answer:
a
[tex]u = 10.11 \ m/s[/tex]
b
[tex]x = 44.996 \ m[/tex]
Explanation:
From the question we are told that
The velocity of the river due east is [tex]v = 1.150i \ m /s[/tex]
The velocity of the boat due north is [tex]v_1 = 10j \ m/ s[/tex]
The width of the river is [tex]d = 300 \ m[/tex]
Generally the velocity of the boat relative to the shore
[tex]u = \sqrt{v^2 + v_1^2}[/tex]
=> [tex]u = \sqrt{1.50 ^2 + 10^2}[/tex]
=> [tex]u = 10.11 \ m/s[/tex]
Generally direction of the boat relative to the shore is mathematically represented as
[tex]tan \theta = \frac{v}{v_1}[/tex]
=> [tex]\theta = tan^{-1}[ \frac{v}{v_1}][/tex]
=> [tex]\theta = tan^{-1}[ \frac{1.5}{10}][/tex]
=> [tex]\theta = 8.53^o[/tex]
Generally the distance covered by the boat in the direction of flow of the river before reaching the north shore is mathematically represented as
[tex]x = d* tan(\theta )[/tex]
=> [tex]x = 300 * tan(8.53)[/tex]
=> [tex]x = 44.996 \ m[/tex]
(a) The velocity of the boat relative to the shore is 10.11 m/s.
(b) The distance traveled by the boat when it reaches the north shore is 303.3 m.
The given parameters;
initial velocity of the river, = 1.5 m/s due eastvelocity of the boat, = 10 m/s due north(a) The velocity of the boat relative to the shore is calculated by applying Pythagoras theorem as shown below;
[tex]v = \sqrt{1.5^2 + 10^2} \\\\v = 10 .11 \ m/s[/tex]
(b) Let the time taken for the boat to reach the north shore = t
[tex]distance = speed \times time \\\\c^2 = a^2 + b^2\\\\[/tex]
the width of the river is the height of the right-trianglethe displacement of the river after time "t" is the base of the right-trianglethe displacement of the boat after time "t" is the hypotenuse side[tex](10.11t)^2 = (300)^2 + (1.5t)^2\\\\102.21t^2 = 90,000 + 2.25t^2\\\\99.96t^2 = 90,000\\\\t^2 = \frac{90,000}{99.96} \\\\t^2 = 900\\\\t = \sqrt{900} \\\\t = 30 \ s[/tex]
The distance traveled by the boat when it reaches the north shore;
[tex]d = 10.11t\\\\d = 10.11 \times 30\\\\d = 303.3 \ m[/tex]
Learn more here:https://brainly.com/question/24430414
In a house, 3 bulbs of 60 watt each are lighted for 3 hours daily, 4 fans of 100 watt each are used for 8 hours daily and an electric heater of 2 kwh used for half an hour daily. Calculate the total energy consumed in a month of 31 days and its cost at the rate of Rs 4/kwh.
Answer:
Total Energy consumed = 146.94 kwh
Total cost = rs 587.76
Explanation:
Given:
3 bulbs each 60 watt [for 3 hours daily]
4 fans each 100 watt [for 8 hours daily
1 electric heater of 2 kWh (2,000 watt) [for half hour daily ]
Rate = rs 4/Kwh
Find:
Total Energy consumed
Total cost
Computation:
Energy used = Power × time
3 bulbs each 60 watt [for 3 hours daily] = 3 x 60 x 3 x 31 = 16,740 watt = 16.74 kw
4 fans each 100 watt [for 8 hours daily = 4 x 100 x 8 x 31 = 99,200 watt = 99.2 kw
1 electric heater of 2 kWh [for half hour daily ] = 1 x 2000 x (1/2) x 31 = 31,000 watt = 31 kw
Total Energy consumed = 16.74 + 99.2 + 31
Total Energy consumed = 146.94 kwh
Total cost = 146.94 x 4
Total cost = rs 587.76
if an atom has two protons and three electrons than the atom is
Answer:
negative 1 charge
Explanation:
one electron is extra so there will be -1 chargw
If an atom has two protons and three electrons than the atom is negatively charged.
What is an atom?An atom is a matter particle that defines a chemical element uniquely. An atom is made up of a central nucleus and one or more negatively charged electrons.
The nucleus is positively charged and contains one or more protons and neutrons, which are relatively heavy particles.
It is made up of protons, which have a positive charge, and neutrons, which do not have any charge. Protons, neutrons, and the electrons that surround them are long-lived particles found in all natural atoms.
The modern atomic hypothesis was founded by John Dalton, a great chemist. His atom, on the other hand, was like a solid billiard ball.
An atom is negatively charged if it has two protons and three electrons.
Thus, the given atom bears negative charge.
For more details regarding atoms, visit:
https://brainly.com/question/1566330
#SPJ2
what is transferred by a radio wave?
A. air
B. energy
C. matter
D. space
(for science)
Answer: B. energy
Explanation:
Please help me on this with a full explanation
Answer:
a = 5 [m/s²]
Explanation:
We must perform a sum of forces on both axes (vertical axis and horizontal axis).
We see that the forces on the vertical axis are the same but in the opposite direction. In this way, there is no movement on the vertical axis y. and we can find the mass of the body.
∑Fy = 0
Fnorm - Fgrav = 0
We know that the force of gravity is equal to the product of mass by gravitational acceleration.
[tex]F_{grav}=m*g[/tex]
where:
m = mass [kg]
g = gravity acceleration = 10 [m/s²]
[tex]100=m*10\\m=100/10\\m=10[kg][/tex]
Since there is only one force on the horizontal axis, this force generates accelerated motion. This force is equal to the product of mass by acceleration, as stipulated by Newton's second law.
∑F = m*a
where:
F = force = 50 [N]
a = acceleration of the body [m/s²]
[tex]F=m*a\\50*10*a\\a=5[m/s^{2} ][/tex]
If you wanted to find a sample of fermium, which has an atomic number of 100, where would you look?
A. Deep within the earth
B. In the earths atmosphere
C. In outer space
D. In Science Lab
Answer:
B
Explanation:
Fermium is a synthetic element with the symbol Fm and atomic number 100. It is an actinide and the heaviest element that can be formed by neutron bombardment of lighter elements, and hence the last element that can be prepared in macroscopic quantities, although pure fermium metal has not yet been prepared.[3] A total of 19 isotopes are known, with 257Fm being the longest-lived with a half-life of 100.5 days.
It was discovered in the debris of the first hydrogen bomb explosion in 1952, and named after Enrico Fermi, one of the pioneers of nuclear physics. Its chemistry is typical for the late actinides, with a preponderance of the +3 oxidation state but also an accessible +2 oxidation state. Owing to the small amounts of produced fermium and all of its isotopes having relatively short half-lives, there are currently no uses for it outside basic scientific research.
Why is the term negative acceleration used instead of deceleration
Answer:
See Explanation
Explanation:
Whenever a force is applied in an object in the opposite direction of its motion. It tends to slow down the speed of the object. Therefore, this force is called the decelerating force and the acceleration produced by it is called deceleration.
The deceleration produced in this case by this decelerating force has a direction opposite to the direction of motion or velocity of the object. Therefore, this deceleration is defined with a negative sign along with its magnitude.
Due to this opposite direction, term negative acceleration is also used instead of deceleration.
Alex, parked by the side of an east-west road, is watching car P, which is moving in a westerly direction. Barbara, driving east at a speed 52 km/h, watches the same car. Take the easterly direction as positive. If Alex measures a speed of 78 km/h for car P, what velocity will Barbara measure?
Answer:
[tex]v_{PB} = 130\ km/h[/tex]
Explanation:
Since, Alex is at rest. Therefore, the speed measured by him will be the absolute speed of car P. Therefore, taking easterly direction as positive:
[tex]Absolute\ Velocity\ of\ Car\ P = v_{P} = -78\ km/h[/tex]
And the absolute velocity of Barbara's Car is given as:[tex]Absolute\ Velocity\ of\ Barbara's\ Car = v_{B} = 52\ km/h[/tex]
Now, for the velocity of Car p with respect to the velocity of Barbara's Car can be given s follows:
[tex]Velocity\ of\ Car\ P\ measured\ by\ Barbara = v_{PB} = v_{B}-v_{P}\\\\v_{PB} = 52\ km/h-(-78\ km/h)[/tex]
[tex]v_{PB} = 130\ km/h[/tex]
An image is a copy of an objecí formed by what light
Answer:
Plane mirror
Explanation:
A virtual image is a copy of an object formed at the location from which the light rays appear to come.
According to Newton's second law, if you increase the mass but the force is the same, what happens to the acceleration?
Audio Recording 50 KB
acceleration decreases
Оа
Ob
Ос
acceleration increases
acceleration remains the same
Simple Answer. Mass cannot change.
Force=Acceleration
One type of gas mixture used in anesthesiology is a 50%/50% mixture (by volume) of nitrous oxide (N2O) and oxygen (O2), which can be premixed and kept in a cylinder for later use. Because these two gases don't react chemically at or below 2000 psi, at typical room temperatures they form a homogeneous single gas phase, which can be considered an ideal gas. If the temperature drops below -6∘C, however, N2O may begin to condense out of the gas phase. Then any gas removed from the cylinder will initially be nearly pure O2; as the cylinder empties, the proportion of O2 will decrease until the gas coming from the cylinder is nearly pure N2O. In a test of the effects of low temperatures on the gas mixture, a cylinder filled at 24.0 ∘C to 2000 psi (gauge pressure) is cooled slowly and the pressure is monitored.
What is the expected pressure at -5.00∘C if the gas remains a homogeneous mixture?
Answer:
1850 psi
Explanation:
You throw a rock from the upper edge of a 88.0 m vertical dam with a speed of 21.0 m/s at 58.0∘ above the horizon. Neglect any effects due to air resistance.
How much time 1 after throwing the rock will it return to its initial height?
how much time t2 after throwing the rock will it hit the water flowing out at the base of the dam
The time taken for the rock to return to its initial height is 6.4 seconds.
The time taken for the rock to hit the water flowing out at the base of the dam is 2.8 seconds.
Time of motion of the rockThe time taken for the rock to return to its initial height is calculated as follows;
h = Vy(t) + ¹/₂gt²
88 = (21 x sin58)(t) + 4.9t²
88 = 17.8t + 4.9t²
4.9t² + 17.8t - 88 = 0
solve the quadratic equation using formula method;
a = 4.9, b = 17.8, c = -88
t₁ = -6.4 seconds
t₂ = 2.8 seconds
The negative time indicates the time taken for the rock to travel back to its initial position.
Also, the positive time indicates the time taken for the rock to fall from the given height.
Thus, the time taken for the rock to return to its initial height is 6.4 seconds.
The time taken for the rock to hit the water flowing out at the base of the dam is 2.8 seconds.
Learn more about time of motion here: https://brainly.com/question/2364404
#SPJ1