Two manned satellites approaching one another at a relative speed of 0.250 m/s intend to dock. The first has a mass of 2.00 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. Assume that the positive direction is directed from the second satellite towards the first satellite.(a) Calculate the final velocity after docking, in the frame of reference in which the first satellite was originally at rest.m/s(b) What is the loss of kinetic energy in this inelastic collision?J(c) Repeat both parts, in the frame of reference in which the second satellite was originally at rest.final velocitym/sloss of kinetic energyJExplain why the change in velocity is different in the two frames, whereas the change in kinetic energy is the same in both. (Do this on paper. Your instructor may ask you to turn in this work.)

The robot moves the particle A (mass M) in the vertical plane using polar coordinate formulas r(t) = 1,2-0,6sin(2πt) [m] θ(t) = 0,5-1,5cos(2πt) [rad] in accordance with Determine the acceleration of the object in the θ direction [m/s2] at time t0=1.9s Use [m/s2] units GIVE ANSWER TO THREE DECIMALS

The following equation describes the motion of a rocket that is expelling a total mass M of fuel at a rateα = -dm/dt:dv/dt = uα/(M-αt),where u is the speed the fuel is ejected, v is the velocity of the rocket in the x-direction, and t is time. Assume the velocity at t = 0 is v(0) = v0, and that M, and u are constants. The burn rate is proportional to the mass of the rocket, as follows:α = -βm,where m is the current mass of the rocket (which is therefore time-dependent). This means that as less fuel is available to burn, then the fuel is burned at a lower rate. Write an expression for the mass of the fuel as a function of time.  Now, write an expression for the velocity as a function of time for the rocket. A particular rocket burns fuel at a rate proportional to the mass of the fuel with the constant of proportionality being 6.4 1/s. The propellant speed is 5.1 m/s. The total mass of fuel is 136.4 kg. What is the speed, in meters per second, of the rocket at t = 2.7 s?

Two manned satellites approaching one another at a relative speed of 0.300 m/s intend to dock. The first has a mass of 4.00 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. Assume that the positive direction is directed from the second satellite towards the first satellite. (a) Calculate the final velocity after docking, in the frame of reference in which the first satellite was originally at rest. ..............m/s

Q.2)

The robot moves the particle A (mass M) in the vertical plane using polar coordinate formulas r(t) = 1,2-0,6sin(2πt) [m] θ(t) = 0,5-1,5cos(2πt) [rad] in accordance with. Determine the acceleration of the body in the r-direction [m / s2] at time t0 = 1.9 s Use units [m/s2] GIVE ANSWER TO THREE DECIMALS

7) Two manned satellites approaching one another, at a relative speed of 0.550 m/s, intending to dock. The first has a mass of 5.00 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg.   (a) Calculate the final velocity (after docking) in m/s by using the frame of reference in which the first satellite was originally at rest. (Assume the second satellite moves in the positive direction. Include the sign of the value in your answer.)  _____m/s   (b) What is the loss of kinetic energy (in J) in this inelastic collision? _____ J   (c) Repeat both parts by using the frame of reference in which the second satellite was originally at rest. final velocity (m/s)  _____ m/s loss of kinetic energy (J) _____ J Explain in detail why the change in velocity is different in the two frames, whereas the change in kinetic energy is the same in both.

A cosmic ray muon with mass  mμ = 1.88 ✕ 10−28 kg  impacting the Earth's atmosphere slows down in proportion to the amount of matter it passes through. One such particle, initially traveling at 2.42 ✕ 106 m/s in a straight line, decreases in speed to 1.60 ✕ 106 m/s over a distance of 1.10 km. (a) What is the magnitude of the force experienced by the muon? N(b) How does this force compare to the weight of the muon? |F| Fg  =

A 1024-kg blue ball is dropped from an initial z-position of 5.8 x 106 m through the center of a planet (earth) with radius 7.1 x 106 m. If the mass of the planet is 41.5 x 1015 kg, measure the displacement of the ball at time t = 4 s?