
Relative to the center of the Earth, the position of the Moon can be approximated by (t) = r [cos (ωt) + sin (ωt) ], where r = 3.84 108 m and ω = 2.46 106 radians/s. (a) Find the magnitude and direction of the Moon's average velocity

The velocity of the Moon relative to the center of the Earth can be approximated by varrowbold(t) = v [−sin (ωt) xhatbold + cos (ωt) yhatbold], where v = 945 m/s and ω = 2.46 multiplied by 10−6 radians/s. (The time required for

Imagine a spaceship on its way to the moon from the earth. Find the point, as measured from the center of the earth, where the force of gravity due to the earth is balanced exactly by the gravity of the moon. This point lies on a line between the centers

The mean distance from the center of the earth to the center of the moon is rem = 3.84 × 108 m. The mass of the earth is me = 5.98 × 1024 kg and the mass of the moon is mm = 7.34 × 1022 kg. The mean radius of the earth is re = 6.37 × 106 m. The mean

A. Use the relation 2 m m m GM g R ƒ to find the acceleration due to gravity on the surface of the Moon. You can use the following data: Mass of the Moon m M = 7.35 ¡Ñ 1022 kg. Radius of the Moon m R = 1.74 ¡Ñ 106 m. B. How does this value compare


Moon effect. Some people believe that the Moon controls their activities. If the Moon moves from being directly on the opposite side of Earth from you to being directly overhead, by what percentage does (a) the Moon's gravitational pull on you increase and

A spacecraft is on a journey to the moon. At what point, as measured from the center of the earth, does the gravitational force exerted on the spacecraft by the earth balance that exerted by the moon? This point lies on a line between the centers of the

A spacecraft is on a journey to the moon. At what point, as measured from the center of the earth, does the gravitational force exerted on the spacecraft by the earth balance that exerted by the moon? This point lies on a line between the centers of the

A spacecraft is on a journey to the moon. At what point, as measured from the center of the earth, does the gravitational force exerted on the spacecraft by the earth balance that exerted by the moon? This point lies on a line between the centers of the

Some people believe that the Moon controls their activities. The Moon moves from being directly on the opposite side of Earth from you to be being directly overhead. Assume that the EarthMoon (centertocenter) distance is 3.82 multiplied by 108 m and

A spaceship of mass 175,000 kg travels from the Earth to the Moon along a line that passes through the center of the Earth and the center of the Moon. At what distance from the center of the Earth is the force due to the Earth twice the magnitude of the

You are flying to the Moon. Find the point at which the gravitational attractions of Earth and Moon on you will be equal and opposite. Given: radius of the moon: 1.74*10^6 m radius of the earth: 6.38*10^6 m orbital radius of the moon: 3.8*10^8 m Not enough

The Moon causes tides because the gravitational force it exerts differs between the side of the Earth nearest the Moon and that farthest from the Moon. Find the difference in the accelerations toward the Moon of objects on the nearest and farthest sides of

The Moon causes tides because the gravitational force it exerts differs between the side of the Earth nearest the Moon and that farthest from the Moon. Find the difference in the accelerations toward the Moon of objects on the nearest and farthest sides of

Suppose that the attraction between the moon and the earth were due to Coulomb forces rather than gravitational force. What would be the magnitude of the charge required if equal but opposite charges resided on both earth and moon? Mass of earth =


How far is the center of mass of the EarthMoon system from the center of the Earth? The Earth's mass is 5.97×1024 kg, the Moon's mass is 7.4×1022 kg, and the distance between their centers is 3.8×108 m.

The average distance separating Earth and the Moon (center to center) is 384 000 km. Use the data in Table 7.3 to find the net gravitational force exerted by Earth and the Moon on a 3.00 multiplied by 104 kg spaceship located halfway between them (Earth

Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1  (3/4)sin^2 2x work on one side only! Responses Trig please help!  Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 x = (sin^2x)^3 +

magine a straight line connecting the centers of the earth and the moon. At some point along this line the gravitational forces pulling a spacecraft towards the moon and towards the earth exactly balance each other, and the craft could just sit there in

Can you please check my work. A particle is moving with the given data. Find the position of the particle. a(t) = cos(t) + sin(t) s(0) = 2 v(0) = 6 a(t) = cos(t) + sin(t) v(t) = sin(t)  cos(t) + C s(t) = cos(t)  sin(t) + Cx + D 6 = v(0) = sin(0) cos(0)

The Moon orbits the Earth at a distance of 3.85 x 108 m. Assume that this distance is between the centers of the Earth and the Moon and that the mass of the Earth is 5.98 x 1024 kg. Find the period for the Moon's motion around the Earth. Express the answer

A spaceship of mass m travels from the Earth to the Moon along a line that passes through the center of the Earth and the center of the Moon. (a) At what distance from the center of the Earth is the force due to the Earth five times the magnitude of the

Calculate the magnitude of the gravitational force between the Earth and an m = 6.00 kg mass on the surface of the Earth. The distance to the center of the Earth from the surface is 6.37×103 km and the mass of the Earth is 5.98×1024 kg. B)Calculate the

expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by b and using that cos(b)= cos(b) sin(b)= sin(b) gives: sin(ab) = sin(a)cos(b)  cos(a)sin(b) Add the two equations:

A spaceship of mass m travels from the Earth to the Moon along a line that passes through the center of the Earth and the center of the Moon. (a) At what distance from the center of the Earth is the force due to the Earth three times the magnitude of the


A canoe has a velocity of 0.480m/s southeast relative to the earth. The canoe is on a river that is flowing at 0.510m/s east relative to the earth. Find the magnitude of the velocity (V(C/R)) of the canoe relative to the river. Also, find the direction of

Choose the two options which are true for all values of x 1) cos (x) = cos ( x – pie/2) 2) sin (x + pie/2) = cos (x – pie/2) 3) cos (x) = sin (x – pie/2) 4) sin (x) = sin (x + 4pie) 5) sin (x) = cos (x – pie/2) 6) sin^2 (x) + cos^2 (x) = pie would

Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y +

1.)Find dy/dx when y= Ln (sinh 2x) my answer >> 2coth 2x. 2.)Find dy/dx when sinh 3y=cos 2x A.2 sin 2x B.2 sin 2x / sinh 3y C.2/3tan (2x/3y) D.2sin2x / 3 cosh 3yz...>> my answer. 2).Find the derivative of y=cos(x^2) with respect to x.

what is the apparent angle the diameterof the moon subtends as seen from the earth in radians. average moon earth distance3.84*10e8 radius of the moon 1.74*10e6

Calculate the magnitudes of the gravitational forces exerted on the Moon by the Sun and by the Earth when the two forces are in direct competition, that is, when the Sun, Moon, and Earth are aligned with the Moon between the Sun and the Earth. (This

Can someone please help me do this problem? That would be great! Simplify the expression: sin theta + cos theta * cot theta I'll use A for theta. Cot A = sin A / cos A Therefore: sin A + (cos A * sin A / cos A) = sin A + sin A = 2 sin A I hope this will

Consider a spaceship located on the EarthMoon center line (i.e. a line that intersects the centers of both bodies) such that, at that point, the tugs on the spaceship from each celestial body exactly cancel, leaving the craft literally weightless. Take

Reduce the following to the sine or cosine of one angle: (i) sin145*cos75  cos145*sin75 (ii) cos35*cos15  sin35*sin15 Use the formulae: sin(a+b)= sin(a) cos(b) + cos(a)sin(b) and cos(a+b)= cos(a)cos(b)  sin(a)sin)(b) (1)The quantity = sin(14575) = sin

I still cannot solve this problem: Consider a spaceship located on the EarthMoon center line (i.e. a line that intersects the centers of both bodies) such that, at that point, the tugs on the spaceship from each celestial body exactly cancel, leaving the


Calculate the position of the center of mass of the following pairs of objects. Use acoordinate system where the origin is at the center of the more massive object. Give youranswer not in meters but as a fraction of the radius as requested. Get data from

Calculate the position of the center of mass of the following pairs of objects. Use acoordinate system where the origin is at the center of the more massive object. Give youranswer not in meters but as a fraction of the radius as requested. Get data from

A series circuit contains a resistor with R = 24 , an inductor with L = 2 H, a capacitor with C = 0.005 F, and a generator producing a voltage of E(t) = 12 sin(10t). The initial charge is Q = 0.001 C and the initial current is 0. Find the charge at time t.

Use the exact values of the sin, cos and tan of pi/3 and pi/6, and the symmetry of the graphs of sin, cos and tan, to find the exact values of si pi/6, cos 5/3pi and tan 4pi/3. I have found the answers to the first three using the special tables

A total solar eclipse occurs when the moon passes between the earth and the sun, and the darkest shadow cast by the moon, called the umbra, hits the surface of the earth. If the umbra does not hit the surface, as shown in the following figure, then a total

Given that the distance between the Earth and the Moon is d = 3.84 108 m, show that a satellite located exactly inbetween the Earth and the Moon at a distance of 90% d from the Earth experiences no net force (at least when only the

The mass of the Moon is 7.35x10 to the 22nd Kg. At some point between the Earth and the Moon, the for of Earth's gravitational attraction on an object is cancelled by the Moon's force of gravitational attraction. If the distance between Earth and the Moon

Consider a spaceship located on the EarthMoon center line (i.e. a line that intersects the centers of both bodies) such that, at that point, the tugs on the spaceship from each celestial body exactly cancel, leaving the craft literally weightless. Take

1.Halley's comet moves about the sun in an elliptical orbit with its closest approach to the sun being 0.59 A.U. and its furthest distance being 35 A.U. [1 Astronomical Unit (A.U.) is the EarthSun distance.] If the comet's speed at closest approach is 54

Consider a spaceship located on the EarthMoon center line (i.e. a line that intersects the centers of both bodies) such that, at that point, the tugs on the spaceship from each celestial body exactly cancel, leaving the craft literally weightless. Take


tan(3x) + 1 = sec(3x) Thanks, pretend 3x equals x so tanx + 1 = secx we know the law that 1 + tanx = secx so tanx + 1 becomes secx and... secx = secx sec(3x) = sec(3x) [just put 3x back in for x you don't really have to change 3x to x but it kinda makes

Use the exact values of the sin, cos and tan of pi/3 and pi/6, and the symmetry of the graphs of sin, cos and tan, to find the exact values of sin pi/6, cos 5/3pi and tan 4pi/3. I have found the answers to the first three using the special tables sin pi/6

still cant get this one? so damon i know you wanna help! or anyone else im open for suggestions haha Consider a spaceship located on the EarthMoon center line (i.e. a line that intersects the centers of both bodies) such that, at that point, the tugs on

Starting from Newton’s law of universal gravitation, show how to find the speed of the moon in its orbit from the earthmoon distance of 3.9 × 108 m and the earth’s mass. Assume the orbit is a circle.

Consider a spaceship located on the EarthMoon center line (i.e. a line that intersects the centers of both bodies) such that, at that point, the tugs on the spaceship from each celestial body exactly cancel, leaving the craft literally weightless. Take

Starting from Newton’s law of universal gravitation, show how to find the speed of the moon in its orbit from the earthmoon distance of 3.9 × 108 m and the earth’s mass. Assume the orbit is a circle. So I calculated this and got 1.0 km/s, I was just

Locate the position of a spaceship on the EarthMoon center line such that, at that point, the tug of each celestial body exerted on it would cancel and the craft would literally be weightless. What is the distance (in m from the moon)

Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v  u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos v + cos v sin u. cos (v 

What is the net gravitational field due the sun and earth at the center of the moon? You are given that the mass of the sun in 1.99 x 10^30 and the mass of the earth is 5.97 x 10^24. The distance from the center of the sun to the center of the earth is

The Moon has a diameter of about 3480 km and an orbital radius of about 384 400 km from the centre of Earth. Suppose that the Moon is directly overhead. What is the measure of the angle subtended by the diameter to the Moon as measured by an astronomer on


Find sin(s+t) and (st) if cos(s)= 1/5 and sin(t) = 3/5 and s and t are in quadrant 1. =Sin(s)cos(t) + Cos(s)Sin(t) =Sin(1/5)Cos(3/5) + Cos(1/5)Sin(3/5) = 0.389418 Sin(st) =sin(s)cos(t)  cos(s)sin(t) =sin(3/5)cos(1/5)  cos(1/5)sin(3/5) =Sin3/5

The diameter of the Moon is 3.78x10^6m. It subtends an angle of .00982 radians at the surface of Earth. How far is the Moon from Earth? (Please explain I can't wrap my head around this question.)

A total solar eclipse occurs when the moon passes between the earth and the sun, and the darkest shadow cast by the moon, called the umbra, hits the surface of the earth. If the umbra does not hit the surface, as shown in the following figure, then a total

The moon is a satellite that orbits the earth at a radius of 3.85 × 108 m. The mass of the earth is 5.98 × 1024 kg. What is the orbital speed of the moon?

On the way from a planet to a moon, astronauts reach a point where that moon’s gravitational pull transitions from being weaker than that of the planet to being stronger than that of the planet. The masses of the planet and the moon are, respectively,

Can someone check my answers? 1. Convert 13pi/30 to degree measure. 78° 2. Find the distance between (4,4) and (8,7). 5 3. What is the vertex of the parabola y = (x + 8)^2  2? (8,2) 4. The graph of y = 6(x  8)^2 + 1 open downward. False. 5. An angle

Your weight on the moon is relative to your weight on Earth. Neil Armstrong weighed 360 lbs. in his moon gear while on Earth, but on the moon he only weighed 60 lbs. What is the ratio of the Earth weight to the moon weight? How much would you weigh

Larry weighs 300 N at the surface of the earth. what is the weight of the earth in the gravitational field of Larry? force= GMm/d^2 would i set it up like force= (9.8m/s^2)(300 N)? an astronaut lands on a planet that has twice the mass as earth and twice

Many astronomers argue that the Earth and Moon should be considered a double planet,since the gravitational force by the sun on the Moon is approximately as big as that by the Earth on the moon.Using the data below for the Earth and Moon at the particular

A satellite is placed between the Earth and the Moon, along a straight line that connects their centers of mass. The satellite has an orbital period around the Earth that is the same as that of the Moon, 27.3 days. How far away from the Earth should this


During a solar eclipse, the moon (of mass 7.36 × 1022 kg), Earth (of mass 5.98 × 1024 kg), and Sun (of mass 1.99 × 1030 kg) lie on the same line, with the moon between Earth and the Sun. What gravitational force is exerted on the moon by the Sun? The

Consider the angle in standard position whose measure is radians. The terminal side of this angle is in the third quadrant and lies on the line given by y=10x. Find sin and cos.

The mass of the Moon is 7.35 x 10^22 kg. At some point between Earth and the Moon, the force of Earth's gravitational attraction on an object is cancelled by the Moon's force of gravitational attraction. If the distance between Earth and the Moon (centre

The Earth has a mass of 5.97 x10^24 kg and the Moon has a mass of 7.36 x10^22kg. The average distance between the center of the Earth and the center of the moon is 3.84 x10^8m. (a) How far away would the Moon need to be for the magnitude of the

Simplify the given expression........? (2sin2x)(cos6x) sin 2x and cos 6x can be expressed as a series of terms that involve sin x or cos x only, but the end result is not a simplification. sin 2x = 2 sinx cosx cos 6x = 32 cos^6 x 48 cos^4 x + 18 cos^2 x 

Calculate the magnitudes of the gravitational forces exerted on the Moon by the Sun and by the Earth when the two forces are in direct competition, that is, when the Sun, Moon and Earth are aligned with the Moon between the Sun and the Earth. This

Given the position function s(t) = t cos t, find the velocity function. Answer v(t) = sin t v(t) = sin t v(t) = cos t  t sin t v(t) = cos t + t sin t

A planet has a single moon that is solely influenced by the gravitational interaction between the two bodies. We will assume that the moon is moving in a circular orbit around the planet and that the moon travels with a constant speed in that orbit. The

Can someone check my answers? 1. Convert 13pi/30 to degree measure. 78° 2. Find the distance between (4,4) and (8,7). 5 3. What is the vertex of the parabola y = (x + 8)^2  2? (8,2) 4. The graph of y = 6(x  8)^2 + 1 open downward. False. 5. An angle

What causes the phases of the moon as observed from the Earth? A) Filtering of the light from the moon due to the Earth's atmosphere. B) The tidal forces of the Earth's oceans change the appearance of the moon. C) Change in distance of the moon from the


2. For an object whose velocity in ft/sec is given by v(t) = t^2 + 6, what is its displacement, in feet, on the interval t = 0 to t = 3 secs? 3. Find the velocity, v(t), for an object moving along the xaxis if the acceleration, a(t), is a(t) = cos(t) 

The main cause of the changing location of the tides on earth is rotation of the Earth on its' own axis  magnetic forces of the Moon  the revolution of the Moon around the Earth *** the position of the Sun

The pull of gravity keeps the Moon in orbit around Earth. The distance between the Earth and Moon is about 380,000 kilometers. A crew of astronauts leaves Earth on a Monday and lands on the Moon on a Thursday. They land on the side of the Moon facing away

The drawing (not to scale) shows one alignment of the sun, earth, and moon. The gravitational force SM that the sun exerts on the moon is perpendicular to the force EM that the earth exerts on the moon. The masses are: mass of sun = 1.99 1030 kg, mass of

The drawing (not to scale) shows one alignment of the sun, earth, and moon. The gravitational force SM that the sun exerts on the moon is perpendicular to the force EM that the earth exerts on the moon. The masses are: mass of sun = 1.99 1030 kg, mass of

The drawing (not to scale) shows one alignment of the sun, earth, and moon. The gravitational force that the sun exerts on the moon is perpendicular to the force that the earth exerts on the moon. The masses are: mass of sun=1.99 × 1030 kg, mass of

The drawing (not to scale) shows one alignment of the sun, earth, and moon. The gravitational force SM that the sun exerts on the moon is perpendicular to the force EM that the earth exerts on the moon. The masses are: mass of sun = 1.99 1030 kg, mass of

A distant galaxy is simultaneously rotating and receding from the earth. As the drawing shows, the galactic center is receding from the earth at a relative speed of uG = 1.90 106 m/s. Relative to the center, the tangential speed is vT = 3.00 105 m/s for

How far is the center of mass of the EarthMoon system from the center of the Earth? The Earth's mass is 5.97e24 Kg, the Moon's mass is 7.4e22 Kg, and the distance between their centers is 3.8e8m.

The mass of the Earth is 5.98x10^24 kg, and the mass of the Moon is 7.36x 10^22 kg. The distance of separation, measured between their centers, is 3.84x10^8 m. Locate the center of mass of the EarthMoon system as measured from the center of the Earth. I


I do not understand how to do this problem ((sin^3 A + cos^3 A)/(sin A + cos A) ) = 1  sin A cos A note that all the trig terms are closed right after there A's example sin A cos A = sin (A) cos (A) I wrote it out like this 0 =  sin^6 A  cos^6 A +

The Moon orbits Earth every 27.3 days. Determine the angular velocity of the Moon, in degrees per day and in radians per day. The radius of the orbit of the Moon is about 384 400 km. How far does the Moon move along an arc of it's orbit every?

still cant get this one? so damon i know you wanna help! or anyone else im open for suggestions haha Consider a spaceship located on the EarthMoon center line (i.e. a line that intersects the centers of both bodies) such that, at that point, the tugs on

A radar antenna is tracking a satellite orbiting the earth. At a certain time, the radar screen shows the satellite to be 159km away. The radar antenna is pointing upward at an angle of 59.3 from the ground.Fine the x and y components(in km) of the

The acceleration acting on a falling object due to gravity varies inversely with the square of the object's distance from the center of Earth. At the surface of Earth, where x = 1 Earth radius, the acceleration is y = 9.8 m/s2 1. Use the multiplymultiply

Find the velocity, v(t), for an object moving along the xaxis if the acceleration, a(t), is a(t) = cos(t)  sin(t) and v(0) = 3 v(t) = sin(t) + cos(t) + 3 v(t) = sin(t) + cos(t) + 2 v(t) = sin(t)  cos(t) + 3 v(t) = sin(t)  cos(t) + 4

Prove that for all real values of a, b, t (theta): (a * cos t + b * sin t)^2 <= a^2 + b^2 I will be happy to critique your work. Start on the left, square it, (a * cos t + b * sin t)^2 = a^2 (1  sin^2t) + 2ab sin t cost+ b^2 (1  cos^2 t)= a^2 + b^2 

You're tour director for a lunar trip, and want to award your passengers with certificates commemorating their crossing the point where the Moon's gravity becomes stronger than Earth's.How far from Earth should you award the certificate? Express your

Please review and tell me if i did something wrong. Find the following functions correct to five decimal places: a. sin 22degrees 43' b. cos 44degrees 56' c. sin 49degrees 17' d. tan 11degrees 37' e. sin 79degrees 23'30' f. cot 19degrees 0' 25'' g. tan

Find the points on the curve y= (cos x)/(2 + sin x) at which the tangent is horizontal. I am not sure, but would I find the derivative first: y'= [(2 + sin x)(sin x)  (cos x)(cos x)]/(2 + sin x)^2 But then I don't know what to do or if that is even


it says to verify the following identity, working only on one side: cotx+tanx=cscx*secx Work the left side. cot x + tan x = cos x/sin x + sin x/cos x = (cos^2 x +sin^2x)/(sin x cos x) = 1/(sin x cos x) = 1/sin x * 1/cos x You're almost there. thanks so

Consider a pulse of laser light aimed at the Moon that bounces back to Earth. The distance between Earth and the Moon is 3.84 * 108 m. Show that the roundtrip time for the light is 2.56 s.

Consider a pulse of laser light aimed at the Moon that bounces back to Earth. The distance between Earth and the Moon is 3.84 * 108 m. Show that the roundtrip time for the light is 2.56 s.

Consider a pulse of laser light aimed at the Moon that bounces back to Earth. The distance between Earth and the Moon is 3.84 * 108 m. Show that the roundtrip time for the light is 2.56 s

calculate the force of gravity between earth (mass = 6.0 x 1024kg) and the moon (mass = 7.4 x 1022 kg). the average Earthmoon distance is 3.8 x 108 m.