A spaceship of mass 110 kg is going to use a planet for a gravitational assist - that is, use the planet's gravity to change its direction of travel without expending any fuel. It is initially moving at a velocity of 230 m/s and at an angle of φ0 = 65°, at a distance 10200 km from the center of the planet as shown in the figure. Give an expression for the angular momentum of the spacecraft, using the coordinate system specified, in terms of m, r0, v0, φ0, and unit vectors i, j, and k. If the spaceship whips around the planet to the other side so that the angle is φ = 45° and is moving at 105 m/s, how far, in kilometers, from the planet is it?

A spaceship of mass 110 kg is going to use a planet for a gravitational assist - that is, use the planet's gravity to change its direction of travel without expending any fuel. It is initially moving at a velocity of 230 m/s and at an angle of φ0 = 65°, at a distance 10200 km from the center of the planet as shown in the figure. Give an expression for the angular momentum of the spacecraft, using the coordinate system specified, in terms of m, r0, v0, φ0, and unit vectors i, j, and k. If the spaceship whips around the planet to the other side so that the angle is φ = 45° and is moving at 105 m/s, how far, in kilometers, from the planet is it?

Related questions

Q: A spaceship of mass 110 kg is going to use a planet for a gravitational assist - that is, use the…

A: Given, Mass of spaceship, m=110kg Velocity, v=230m/s φ0=65° Distance, d=10200×103m a. Angular…

Q: A cockroach of mass m lies on the rim of a uniform disk of mass 7 m that can rotate freely about its…

A: Angular momentum, L = I ω Where, I = moment of inertia ω = angular velocity As angular momentum is…

Q: Consider a spacecraft orbiting Earth. At an instant in time, the angular velocity of the spacecraft…

A: Given, The angular velocity of spacecraft with respect to earth is, ω→=1.6b^1+0.52b^2+0.21b^3 rad/s…

Q: Two particles, each of mass 2.75 × 104 kg and speed 7.10 m/s, travel in opposite directions along…

A: Since you have posted a question with a multiple sub parts, we will solve first three sub - parts…

Q: A spherical satellite of approximately uniform density with radius 5.7 m and mass 240 kg is…

A: Given:- Aspherical satellite of approximately uniform density with radius r = 5.7 m and mass m=…

Q: A cockroach of mass m lies on the rim of a uniform disk of mass 7 m that can rotate freely about its…

A: Given that: Mass of cockroach, mc=m Mass of disk, md=7m Radius of the disk=R ω=0.324 rad/s

Q: An airplane of mass 4.0 × 104 kg flies horizontally at an altitude of 10 km with a constant speed of…

A: a. consider that

Q: Consider a spacecraft orbiting Earth. At an instant in time, the angular velocity of the spacecraft…

A: Given data, Angular velocity of the spacecraft relative to Earth :- ω→=1.6b^1+0.77b^2+0.39b^3…

Q: What is the angular momentum (in kg*m*m/s) of a 350 g symmetrical rotating bar which is 4.50 m long…

A: Given, Mass of symmetrical bar (m) = 0.350kg Length of bar (L) = 4.50m Bar is rotating about…

Q: Consider a spacecraft with moment of inertia matrix (in terms of body axis) given by: 5000 0.0 0.0…

A: Given: The value of I1=5000 kg.m2. The value of I2=10000 kg.m2. The value of…

Q: Consider a tennis ball that is hit by a player at the baseline with a horizontal velocity of 45 m/s…

Q: y 00

A: First we calculate angular momentum and directions or velocity or distance Angular momentum=…

Q: A stirng is attached to a tennis ball and it is swung around in a circular path. If the angular…

A: angular velocity ω=12.7 rad/s length of string l=34 cm=0.34 m

Q: A space of mass 120 kg is going to use a planet for a gravitational assist- that is, use the…

Q: We have a non-rotating space station in the shape of a long thin uniform rod of mass 6.38 x 10^6 kg…

Q: Consider two blocks glued to the top of a disk that is turning at a non-zero angular speed, one…

Q: A merry-go-round is a playground ride that consists of a large disk mounted to that it can freely…

Q: (a) Calculate the angular momentum (in kg m²/s) of Neptune in its orbit around the Sun. (The mass of…

Q: What is the angular momentum of the moon around the earth? The moon’s mass is 7.4 x 1022 kg and it…

A: The angular momentum is given by; L=mvr Here, m is mass of moon , v is speed of moon and r is…

Q: (a) Calculate the angular momentum (in kg · m2/s) of Jupiter in its orbit around the Sun. (The mass…

Q: An object with mass=1.0kg is projected vertically up with speed vo=10 m/s from a point with…

A: Basic Details The change in the angular momentum is the difference between the final and the initial…

Q: wo particles, each of mass 3.21 x 10-4 kg and speed 6.81 m/s, travel in opposite directions along…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Consider a particle A of mass ma = 9 kg moving at a velocity JA = 3 i + 3 j m/s and a particle B of…

Q: that consists of a large disk mounted to that it can freely rotate in a horizontal plane. The…

Q: Find the angular momentum (in kg · m2/s) of Saturn in its orbit around the Sun. - The mass of Saturn…

Question

Give an expression for the angular momentum of the spacecraft, using the coordinate system specified, in terms of m, r₀, v₀, φ₀, and unit vectors i, j, and k.

If the spaceship whips around the planet to the other side so that the angle is φ = 45° and is moving at 105 m/s, how far, in kilometers, from the planet is it?

Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

GIVEN:

VIEW

INITIAL CALCULATIONS:

SOLUTION PART-1:

SOLUTION PART-2:

ANSWER:

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

A circular space station with a radius of 72 m has just been completed. In order to provide astronauts with the feeling of gravity, the space station will be set spinning about its central axis. To do this, solid fuel rockets have been attached around the perimeter of this station to start it spinning. These rockets fizzle out quickly, and produce a non-uniform angular acceleration of =a0e−bt Where a0 = 0.0424 rad/s2 and b = 0.153 s-1. The station is at rest (is not spinning) when the rockets are ignited at t = 0 s. What is the tangential speed of the outer edge of the station about the center of the station at t = 6.27 s? Through what angle has the station rotated in that time? Once the rockets are done burning, how long does it take the station to complete one revolution?
A 1500-kg satellite orbits a planet in a circular orbit of radius 6.2 × 106 m. What is the angular momentum, in kg m2/s, of the satellite in its orbit around the planet if the satellite completes one orbit every 1.5 × 104 s?
A boy of mass m runs with speed v tangentially toward a merry-go-round of mass M and radius R, which is rotating with angular speed w. If the boy jumps on the merry-go-round, find the angular speed with which the system rotates once the boy is on top of the merry-go-round.
Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. A star with a of mass of 2.0x1032 kg and radius 7.0x108 m is initially rotating at a rate of once every 30 days. The star collapses into a neutron star with the same mass but a new radius of 16,000 m. What is the angular speed of the star? (Give your answer in rotations per second.) Assume the star is a solid sphere: Isphere = 2/5 MR2. The Crab Nebula (shown below) formed from a nearby supernova (6000 light years away). Chinese astronomers observed the event in the year 1054 and since that time the nebula has been expanding into what it appears like today. The Crab Pulsar is a neutron star at the center of the nebula and the remains of the original supernova.
While you are on an archaeological dig in Egypt, you observe a scarab beetle of mass m lies on the rim of a uniform disk of mass 3.80m (3.8 times the mass of the beetle) that can rotate freely about its center like a merry-go-round. Initially, the beetle and disk rotate together with an angular velocity of 0.230 rad/s. Then the beetle walks halfway to the center of the disk. (a) what then is the angular velocity of the beetle-disk system?
A thin circular hoop made of tungsten is rotating about its axis.Two copper beads are gently attached to the opposite ends of adiameter of the tungsten hoop. Mass of tungsten hoop is m.Mass of each copper bead is M. The angular velocitiesbefore and after attachment of the copper beads are ω and ω',respectively. Find the final angular velocity ω'. (a)ω(m+2M)/m (b)ω(m-2M)/(m+2M) (c)ωm/(2m+M) (d)ωm/(m+2M).
A spherical satellite of approximately uniform density with radius 4.8 m and mass 215 kg is originally moving with velocity (2600, 0, 0) m/s, and is originally rotating with an angular speed 2 rad/s, in the direction shown in the diagram. A small piece of space junk of mass 6.0 kg is initially moving toward the satellite with velocity (-2200, 0, 0) m/s. The space junk hits the edge of the satellite as shown in the figure below, and moves off with a new velocity ( 1300, 480, 0) m/s. Both before and after the collision, the rotation of the space junk is negligible. V3 L Part 1 Ux = Uy = @1 (a) Just after the collision, what are the components of the center-of-mass velocity of the satellite (v, and vy) and its rotational speed w? (For Ux, enter your answer to at least four significant figures.) Part 2 Mi @= i i Save for Later i M, R, 1 V2 m m/s m/s rad/s (b) Calculate the rise in the internal energy of the satellite and space junk combined. J Attempts: 0 of 10 used Submit Answer
A man with a mass Of 80 kg runs at a speed of 4 m/s along the tangent to a disk shaped platform of mass 160 kg and radius of 2 m. The platform is initially at rest but can rotate freely about an axis through its center. For the platform, I = (1/2) M R². Treat the man as a point particle. (a) Find the angular velocity of the platform after the man jumps in. (2) He then walks slowly to the center. Find the new angular velocity.
A planet is at a position of r→=3.0×10^12mx̂ − 4.0×10^12mŷ as it moves in an elliptical orbit around a large star at the origin (x=0, y=0). If the planet has a mass of 6.0 ×1026 kg and is moving with a velocity of v→=9.5km/sx̂, what is its angular momentum vector? (give magnitude and direction)
Consider a spacecraft orbiting Earth. At an instant in time, the angular velocity of the spacecraft relative to Earth is = 1.9bh +0.82b2+0.34b3 (in rad/s) and the angular acceleration of the spacecraft relative to Earth is a = 0.0561 +0.19bz+0.22bg (in rad/s?). What is the moment (in N.m) being applied on the spacecraft in the b2. Assume the moment of inertia of the spacecraft is given by: Г5000 0.0 0.0 0.0 10000 0.0 kg.m? 0.0 13000 Note b1, b2, bz are unit vectors fixed in the spacecraft reference frame.
A bicycle is traveling north at 6.84 m/s. The mass of the wheel, 2.6 kg, is uniformly distributed along the rim(I=mr2), which has a radius of 17.89 cm. What are the magnitude(in kg m2/s) and direction of the angular momentum of the wheel about its axle?
An object of mass 2.75 kg is moving with a velocity v = (3.8of – 5.10k) m/s. What is the angular momentum of the mass relative to the origin when it is at the location (1.50, -1.50, 1.50) m? (Express your answer in vrector form )