A 0.26 kg rock is thrown vertically upward from the top of a cliff that is 32 m high. When it hits the ground at the base of the cliff, the rock has a speed of 29 m/s. Assuming that air resistance can be ignore and using conservation of mechanical energy, find (a) the initial speed of the rock and (b) the greatest height of the rock as measured from the base of the cliff.

Answers

Answer 1

Answer:

Answer:

a) The initial speed of the rock is approximately 14.607 meters per second.

b) The greatest height of the rock from the base of the cliff is 42.878 meters.

Explanation:

a) The rock experiments a free-fall motion, that is a vertical uniform accelerated motion due to gravity, in which air friction and effects of Earth's rotation. By Principle of Energy Conservation we have the following model:

$U_(g,1)+K_(1) = U_(g,2)+K_(2)$ (Eq. 1)

Where:

$U_(g,1)$ , $U_(g,2)$ - Initial and final gravitational potential energies, measured in joules.

$K_(1)$ , $K_(2)$ - Initial and final translational kinetic energies, measured in joules.

By definitions of gravitational potential and translational kinetic energies we expand and simplify the equation above:

$m\cdot g\cdot (y_(1)-y_(2))= (1)/(2)\cdot m\cdot (v_(2)^(2)-v_(1)^(2))$

$g\cdot (y_(1)-y_(2)) = (1)/(2)\cdot (v_(2)^(2)-v_(1)^(2))$ (Eq. 2)

Where:

$g$ - Gravitational acceleration, measured in meters per square second.

$y_(1)$ , $y_(2)$ - Initial and final height, measured in meters.

$v_(1)$ , $v_(2)$ - Initial and final speed of the rock, measured in meters per second.

If we know that $g = 9.807\,(m)/(s^(2))$ , $y_(1) = 32\,m$ , $y_(2) = 0\,m$ and $v_(2) = 29\,(m)/(s)$ , then the equation is:

$\left(9.807\,(m)/(s^(2)) \right)\cdot (32\,m-0\,m) = (1)/(2)\cdot \left[\left(29\,(m)/(s) \right)^(2)-v_(1)^(2)\right]$

$313.824 = 420.5-0.5\cdot v_(1)^(2)$

$0.5\cdot v_(1)^(2) = 106.676$

$v_(1) \approx 14.607\,(m)/(s)$

The initial speed of the rock is approximately 14.607 meters per second.

b) We use (Eq. 1) once again and if we know that $g =9.807\,(m)/(s^(2))$ , $y_(1) = 32\,m$ , $v_(1) \approx 14.607\,(m)/(s)$ and $v_(2) = 0\,(m)/(s)$ , then the equation is:

$\left(9.807\,(m)/(s^(2)) \right)\cdot (32\,m-y_(2)) = (1)/(2)\cdot \left[\left(0\,(m)/(s) \right)^(2)-\left(14.607\,(m)/(s) \right)^(2)\right]$

$313.824-9.807\cdot y_(2) = -106.682$

$9.807\cdot y_(2) = 420.506$

$y_(2) = 42.878\,m$

The greatest height of the rock from the base of the cliff is 42.878 meters.

Related Questions

A string is attached to the rear-view mirror of a car. A ball is hanging at the other end of the string. The car is driving around in a circle, at a constant speed. Which of the following lists gives all of the forces directly acting on the ball?a. tensionb. tension and gravityc. tension, gravity, and the centripetal forced. tension, gravity, the centripetal force, and friction
If the diameter of the black marble is 3.0cm, and bye using the formula for volume, what is a good approximation if it’s volume? Record to the ones place
Feest. Fysics and motion11Select the correct answerYou travel in a circle, whose circumference is 8 kilometers, at an average speed of 8 kilometers/hour. If you stop at the same point you startedfrom, what is your average velocity?A0 kilometers/hourB.2 kilometers/hour4 kilometers/hourD8 kilometers/hourE.16 kilometers/hourRese
How long does it take a wheel that is rotating at 33.3 rpm to speed up to 78.0 rpm if it has an angular acceleration of 2.15 rad/ s 2?
URGENT!!!!!! Assume that a wire has 1.5 ohms of resistance. If the wire is connected to two batteries with a total voltage of 3.0 V, how much current will flow through the wire? 3.0 amps 2.3 amps 2.0 amps 1.0 amps

Which of these objects are constantly in motion? Select all that apply.A.
Earth

B.
Planes

C.
Trains

D.
Blood

E.
Sun

F.
Cars

Answers

The object Earth,Sun, and Blood are constantly in motion. The correct option is A, D, and E.

What is motion?

if a body changes its position with respect to its surroundings in a given interval of time, Then the body is said to be in motion

Motion is generally classified as follows.:

i) Rectilinear motion.

ii) Circular motion.

iii) Rotational motion.

iv) Periodic motion.

The Earth is continuously in motion because it continuously revolves around The Sun in an elliptical orbit, due to which a year is 365 days. and also The earth rotates about its own axis once a day.

The Sun also revolves around the galactic center of our Milkyway galaxy. and it also rotates about its own axis continuously. so that the sun is also continuously in motion.

The Human blood is continuously in motion Because our blood is continuously circulating whole over the body with the help of our heart. The heart continuously pumps our blood and circulates it inside the human body.

Hence the Earth, Sun, and blood are continuously in motion.

To learn more about Motion click:

brainly.com/question/22810476

#SPJ3

earth, blood, and the sun

A syringe containing 12.0 mL of dry air at 25 C is placed in a sterilizer and heated to 100.0 C. The syringe is sealed, but the plunger can move and the volume can change. What is the volume of the air in the syringe at 100.0 C, assuming no change in pressure?

Answers

Answer:

15.01 Liters

Explanation:

T₁ = Initial temperature = 25°C = 298.15 K

T₂ = Final temperature = 100°C = 373.15 K

V₁ = Initial volume = 12 mL

Here, pressure is constant so we apply Charles Law

$(V_1)/(T_1)=(V_2)/(T_2)\n\Rightarrow {V_2}=(V_1)/(T_1)* T_2\n\Rightarrow {V_2}=(12)/(298.15)* 373.15\n\Rightarrow {V_2}=15.01 L$

∴ Final volume at 100°C is 15.01 Liters.

A series circuit contains a 20-Ω resistor, a 200-mH inductor, a 10-μF capacitor, and an ac power source. At what frequency should the power source drive the circuit in order to have maximum power transferred from the driving source?

Answers

Answer:

f = 113 Hz

Explanation:

In order to have maximum power transferred from the driving source, as the RMS voltage doesn´t depends on frequency, the current I must be maximum.

This condition is met when the circuit behaves a purely resistive, as the impedance is at a minimum.

Such condition is known as resonance, and it satisfies the following equation:

XL = XC ⇒ ω₀ * L = 1 / ω₀*C, where ω₀, is the angular frequency at resonance.

Solving for ω₀, we have:

ω₀ = 1/√LC = 1/√200*10⁻3 H* 10⁻6F = 707 rad/sec

As we need to find the frequency (in cycles/sec), we need to convert from angular frequency to frequency, as follows:

ω₀ = 2*π*f₀ ⇒ f₀ = ω₀ / 2*π = 707 rad/sec / 2*π rad = 113 Hz

A concave mirror is to form an image of the filament of a headlight lamp on a screen 8.50 m from the mirror. The filament is 6.00 mm tall, and the image is to be 37.5 cm tall. Part A: How far in front of the vertex of the mirror should the filament be placed?Part B: to what radius of curvature should you grind the mirror?

Answers

Answer:13.6 cm

Explanation:

Given

v(image distance)=-8.5 m

height of object $(h_1)$ =6 mm

height of image $(h_2)$ =37.5 cm

and magnification of concave mirror is given by $m=(-v)/(u)=(-h_2)/(h_1)$

$m=(-37.5* 10)/(6)=-62.5$

$-62.5=(8.5* 100)/(u)$

u=13.6 cm

so object is at a distance of 13.6 cm from mirror.

for focal length

$(1)/(f)=(1)/(v)+(1)/(u)$

$(1)/(f)=(-1)/(850)+(-1)/(13.6)$

$(1)/(f)=-0.00117-0.0735$

f=-13.4 cm

thus radius of curvature of mirror is R=2f=26.8 cm

Final answer:

The filament of the headlight lamp should be placed about 0.85 m in front of the vertex of the mirror. The radius of curvature for the concave mirror should be approximately 0.85 m.

Explanation:

To determine how far in front of the vertex of the mirror the filament should be placed, we can use the mirror equation:

1/f = 1/do + 1/di

Where f is the focal length of the concave mirror, do is the object distance, and di is the image distance.

With the given information, we have:

do = ?

di = 8.50 m

Using the magnification formula:

magnification = -di/do

By substituting the values we know, we can solve for do:

37.5 cm / 6.00 mm = -8.50 m / do

Solving for do, we find that do ≈ - 0.85 m.

Since the object distance cannot be negative, we conclude that the filament of the headlight lamp should be placed about 0.85 m in front of the vertex of the mirror.

To find the radius of curvature for the concave mirror, we use the mirror formula:

1/f = 1/do + 1/di

With do = -0.85 m and di = 8.50 m, we can rearrange the formula to solve for f:

1/f = 1/-0.85 + 1/8.50

1/f ≈ -1.1765

Solving for f, we find that the focal length is approximately 0.85 m.

Learn more about Concave mirror here:

brainly.com/question/3555871

#SPJ3

The type of function that describes the amplitude of damped oscillatory motion is _______. The type of function that describes the amplitude of damped oscillatory motion is _______. quadratic sinusoidal inverse exponential linear

Answers

Answer:

exponential

Explanation:

type of function that describes the amplitude of damped oscillatory motion is exponential because as we know that here function is

y = A × $e^{(-bt)/(2m)}$ × cos(ωt + ∅ ) ..................................... ( 1 )

here function A × $e^{(-bt)/(2m)}$ is amplitude

as per equation ( 1 )it is exponential

so that we can say that amplitude of damped oscillatory motion is exponential

According to the second law of thermodynamics, it is impossible for ____________. According to the second law of thermodynamics, it is impossible for ____________. heat energy to flow from a colder body to a hotter body an ideal heat engine to have the efficiency of 99% an ideal heat engine to have non-zero power. a physical process to yield more energy than what is put in

Answers

Answer:

It's impossible for an ideal heat engine to have non-zero power.

Explanation:

Option A is incomplete and so it's possible.

Option B is possible

Option D is related to the first lae and has nothing to do with the second law.

Hence, the correct option is C.

The ideal engine follows a reversible cycle albeit an infinitely slow one. If the work is being done at this infinitely slow rate, the power of such an engine is zero.

We can also stat the second law of thermodynamics in this manner;

It is impossible to construct a cyclical heat engine whose sole effect is the continuous transfer of heat energy from a colder object to a hotter one.

This statement is known as second form or Clausius statement of the second law.

Thus, it is possible to construct a machine in which a heat flow from a colder to a hotter object is accompanied by another process, such as work input.

Final answer:

According to the second law of thermodynamics, it is impossible for heat energy to flow from a colder body to a hotter body, for an ideal heat engine to have an efficiency of 99%, and for a physical process to yield more energy than what is put in.

Explanation:

According to the second law of thermodynamics, it is impossible for heat energy to flow from a colder body to a hotter body. This is because heat naturally flows from a region of higher temperature to a region of lower temperature. This principle is what allows us to effectively use heat for various purposes, such as in heat engines.

An ideal heat engine is a theoretical construct used to study the efficiency of engines. The second law of thermodynamics states that no heat engine can have an efficiency of 100%, so it is impossible for an ideal heat engine to have an efficiency of 99%. This is due to the losses in heat transfer and other thermodynamic processes.

The second law of thermodynamics also implies that in any physical process, the total energy cannot increase. It is impossible for a physical process to yield more energy than what is put in. This principle is central to understanding energy conservation and the limitations of energy conversion.

Learn more about Second Law of Thermodynamics here:

brainly.com/question/32826461

#SPJ3

Other Questions

The wind-chill index is modeled by the function W = 13.12 + 0.6215T − 11.37v0.16 + 0.3965Tv0.16 where T is the temperature (°C) and v is the wind speed (km/h). When T = 12°C and v = 18 km/h, by how much would you expect the apparent temperature W to drop if the actual temperature decreases by 1°C? (Round your answers to two decimal places.)

A 1,200 kg car travels at 20 m/s. what is it’s momentum ?

Most elements in nature exist as mixture of two or more isotopest or f

While the block hovers in place, is the density of the block (top left) or the density of the liquid (bottom center) greater?