A space vehicle is traveling at 3840 km/h relative to Earth when the exhausted rocket motor is disengaged and sent backward. The relative speed between the motor and the command module is then 94 km/h. The mass of the motor is four times the mass of the module. What is the speed of the command module relative to Earth just after the separation? Number i Units

Center of Mass. c) The mass of the Sun is 2x1030 kg. The distance between the Earth and the Sun is 1.5x108 km. How does the distance between the CM of this system compare to the Sun’s radius of 700,000 km?

An object of mass 310 kg goes past a planet of mass 5 x 1022 kg at a distance of 5 x 106 m from the center of the planet, traveling at a speed of 1230 m/s. Part 1 How far from the center of the planet will the object be when its speed is 1000 m/s? Distance = i m Save for Later Attempts: 0 of 4 used Submit Answer Part 2 Is the system consisting of the planet and the object in a bound state or an unbound state? bound O unbound

A satellite is in a circular orbit of radius r around the Earth. (Use the following as necessary: G, ME, and r.) a) Determine an expression that will allow you to find the speed of the satellite. b)The satellite splits into two fragments, with masses m and 4m. The fragment with mass m is initially at rest with respect to the Earth, then falls straight towards the Earth. The fragment with mass 4m moves with initial speed vi. Find an expression for vi. c)Because of the increase in its speed, this larger fragment now moves in an elliptical orbit. Find an expression for the fragment's distance away from the center of the Earth when it reaches the far end of the ellipse.

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A puck of mass m=2 kg moves on a circle of radius r=0.5 meters, on a frictionless table. The puck is attached to an object of mass M=10 kg by a cord that extends through a hole on the table. Find the speed of the puck if the object is at rest. You may take g=10m/s². Select one: O a. 4/3m/s O b.5/2m/s O c. 5m/s O d. 25m/s O e. 4m/s

1. Consider a mass m initially at rest at a large distance I from center of the earth (l>R the earth's radius). The mass m is released and falls toward the earth. (a) Calculate the speed of the mass as a function of its distance x from the center of the earth. (b) In the approximation that l>>R, how much time does it take for the mass m to reach the earth? Express your answers in terms of R, 1, g (acceleration at the earth's surface) and (for part a) x.

A binary star consist of two stars of the same mass m revolving in a circle of radius R about their common centre of mass. Suppose that a meteorite passes through the centre of mass of the binary star in a direction perpendicular to the orbital plane. What is the minimum speed that the meteorite must have at the centre of mass in order for it to escape from the gravitational attraction of the binary star? ANSW: 4Gm R w

A meteoroid is moving towards a planet. It has mass m = 0.54×109 kg and speed v1 = 4.7×107 m/s at distance R1 = 1.6×107 m from the center of the planet. The radius of the planet is R = 0.78×107 m. The mass of the planet is M = 5.6×1025kg. There is no air around the planet.  a)Enter an expression for the total energy E of the meteoroid at R, the surface of the planet, in terms of defined quantities and v, the meteoroid’s speed when it reaches the planet’s surface. Select from the variables below to write your expression. Note that all variables may not be required.α, β, θ, d, g, G, h, m, M, P, R, R1, t, v, v1 b)Enter an expression for v, the meteoroid’s speed at the planet’s surface, in terms of G, M, v1, R1, and R. c)Calculate the value of v in meters per second.

Current Attempt in Progress An object, with mass 27 kg and speed 22 m/s relative to an observer, explodes into two pieces, one 4 times as massive as the other; the explosion takes place in deep space. The less massive piece stops relative to the observer. How much kinetic energy is added to the system during the explosion, as measured in the observer's reference frame? Number i Units