An astronaut in her space suit has a total mass of m₁ = 89.0 kg, including suit and oxygen tank. Her tether line loses its attachment to her spacecraft while she's on a spacewalk. Initially at rest with respect to her spacecraft, she throws her oxygen tank of mass m₂ = 12.0 kg away from her spacecraft with a speed v = 7.50 m/s to propel herself back toward it (see figure). m₂ m₂ (a) Determine the maximum distance she can be from the craft and still return within 2.40 min (the amount of time the air in her helmet remains breathable). (b) Explain in terms of Newton's laws of motion why this strategy works.

An astronaut in her space suit has a total mass of m₂ = 83.0 kg, including suit and oxygen tank. Her tether line loses its attachment to her spacecraft while she's on a spacewalk. Initially at rest with respect to her spacecraft, she throws her oxygen tank of mass m₂ = 12.0 kg away from her spacecraft with a speed v = 7.50 m/s to propel herself back toward it (see figure). $ (a) Determine the maximum distance she can be from the craft and still return within 1.80 min (the amount of time the air in her helmet remains breathable). m (b) Explain in terms of Newton's laws of motion why this strategy works.

Identical twins, each with mass 52.5 kg, are on ice skates and at rest on a frozen lake, which may be taken as frictionless. Twin A is carrying a backpack of mass 12.0 kg. She throws it horizontally at 2.55 m/s to Twin B. Neglecting any gravity effects, what are the subsequent speeds of Twin A and Twin B?

There are two particles (1 and 2) that are moving around in space. The mass of particle 1 is 2.8 kg and the mass ofparticle 2 is 1.96 kg. The particles are isolated so that only the forces between the particles are significant. The forcethat 2 exerts on 1 is given by:~F21(t) = Fat ˆi + Fbt3 ˆjThe initial time is ti = 4.1 s and the final time is tf = 6.8 s.Use the following values for the parameters:Fa = -18.4 N/s , Fb = 11.2 N/s3, If the y component of the impulse from 1 on 2 is -5196 N s, what is the y component of the change in momentum forparticle 2?

Problem 3: A particle with mass ma = 3.00 kg is located at ra = (2.50 i + 3.50 j) m, and a second particle of mass m2B = 5.00 kg is located at rB = (1.50 i - 3.00 j) m. Find the location of the center of mass of the system relative to the point (1,1).

A system of three particles with masses m1 = 3.0 kg, m2 = 4.0 kg and m3 = 8.0 kg is placed on a two dimensional xy plane. The scales on the axes are set by x, = 2.0 m and y, = 2.0 m. y (m) mg m1 * (m) Figure 2 (a) Find out the x coordinate of the system's center of mass. (b) Find out the y coordinate of the system's center of mass. (c) Find out the acceleration of the system if an external force of 5 N acts on it.

A 2.06-kg particle has a velocity (1.92 î − 2.98 ĵ) m/s, and a 2.90-kg particle has a velocity (1.06 î + 5.93 ĵ) m/s. (a) Find the velocity of the center of mass.   (b) Find the total momentum of the system.

A rocket, which is in deep space and initially at rest relative to an inertial reference frame, has a mass of 72.9 x 105 kg, of which 14.7 x 10° kg is fuel. The rocket engine is then fired for 300 s, during which fuel is consumed at the rate of 360 kg/s. The speed of the exhaust products relative to the rocket is 3.82 km/s. (a) What is the rocket's thrust? After the 300 s firing, what are (b) the mass and (c) the speed of the rocket? (a) Number i Units (b) Number Units (c) Number i Units

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A rocket, which is in deep space and initially at rest relative to an inertial reference frame, has a mass of 78.4 × 105 kg, of which 8.68 × 105 kg is fuel. The rocket engine is then fired for 340 s, during which fuel is consumed at the rate of 340 kg/s. The speed of the exhaust products relative to the rocket is 3.78 km/s. (a) What is the rocket's thrust? After the 340 s firing, what are (b) the mass and (c) the speed of the rocket? (a) Number 1290000 Units N (b) Number 7720000 Units kg (c) Number 3830 Units m/s