Question

Two astronauts (lets say George and Sandra) are drifting somewhat towards one another while in deep space, as shown. Specifically, George is moving with speed V_g, and Sandra is moving with speed V_s = 8 V_g/5 . When George and Sandra collide with one another, they hang on tight and move off in the same direction with speed V_f = V_g/2. George has mass m_g = 1.60 m_s where m_s is Sandras mass.

(a) What are the magnitude P_g of Georges momentum, P_s the magnitude of Sandras momentum, and P_f the magnitude of their combined final momentum. Express your answers in terms of m_s and V_g.

(b) Chose a coordinate system for this problem, and draw arrows representing the vectors P_g, P_s , and P_f. Be sure to include angles to represent the momentum directions. Define any and all symbols that you introduce. (Hint: A clever choice of coordinate system here will simplify the rest of this problem a great deal.)

(c) Using the diagram that you drew for part (b), determine the angle ₀ at which the two astronauts collided.

Two astronauts (let's say George and Sandra) are drifting somewhat towards one another while in deep space, as shown. Specifically, George is moving with speed Vg, and Sandra is moving with speed Vs = 8 Vg/5 . When George and Sandra collide with one another, they hang on tight and move off in the same direction with speed Vf = Vg/2. George has mass mg = 1.60 ms where ms is Sandra's mass. (a) What are the magnitude Pg of George's momentum, Ps the magnitude of Sandra's momentum, and Pf the magnitude of their combined final momentum. Express your answers in terms of ms and Vg. (b) Chose a coordinate system for this problem, and draw arrows representing the vectors Pg, Ps , and Pf. Be sure to include angles to represent the momentum directions. Define any and all symbols that you introduce. (Hint: A clever choice of coordinate system here will simplify the rest of this problem a great deal.) (c) Using the diagram that you drew for part (b), determine the angle Theta0 at which the two astronauts collided. (d) Clearly this collision is completely inelastic because the two astronauts ''stick together'', but just how inelastic is the collision? In other words, by what percent has their kinetic energy decreased?

(d) Clearly this collision is completely inelastic because the two astronauts stick together, but just how inelastic is the collision? In other words, by what percent has their kinetic energy decreased?

Answer 1

2 Mg Final momen hum axrs

In the part (b), it is convenient to consider the coordinates X,Y such a way that, the Y axis is taken along Pf

r dire etion 1-3 133 0 132 Percentee decrement /kEmhal KE KE KE; 2.

Here, the initial kinetic energy of both George and Sandra are found, and then by subtracting the final kinetic energy of the combined bodies, the difference between the initial and final kinetic energy is found, then the percentage decrement is found.

2- 2 ½(2.6 ms)(2) 2 -D, 325 ms =29.1.