Question 3.) Lurking 3. Lurking: You are the captain of a spaceship exploring a

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Question 3.) Lurking 3. Lurking: You are the captain of a spaceship exploring a star system consisting of two visible stars, one a blue giant with a mass of 11M and the other a red dwarf with a mass of about 0.5M (where M is the mass of our sun). Earlier missions reported that the system also contains a small black hole of mass 2M, but the black hole is not visible and you are unsure exactly where it is. You define a reference frame fixed to your ship, with yourself at the origin, the x- axis pointing towards the blue star, and the x-y plane containing both stars. The blue giant is 700 Gm away from you along your x-axis, while the red dwarf is 825 Gm away from you in a direction 14 from the x-axis in the -y direction (i.e., in the fourth quadrant) a) Draw a picture of the situation, and find both stars' position vectors in component form b) At Starfleet Academy, you learned that stellar system tend to form in such a way that their members' orbits (1) are approximately circular about the system's center of mass, (2) all lie in the same plane, and (3) all orbit in the same direction (clockwise or counterclockwise). Your measurements indicate that the blue giant is moving directly in the +y direction, while the red dwarf is moving 45 between +x and +y. Assuming that you are at rest with respect to the system's center of mass, estimate the location of the system's center of mass c) Given these assumptions, locate the black hole and estimate its current direction of motion. Are you safe at your present location, or should you panic? 4. smashing: You are the physics consultant for a Hollywood movie. For one scene, the director wants a 750 kg car traveling due east at 35 m/s to collide with a 3200 kg truck traveling due north. She wants the collision to be arranged so that just after the collision, the interlocked vehicles travel straight towards the camera, which is located a safe distance away along a line that makes an angle of respect to north. At what speed should the trucker drive?

Explanation / Answer

4)

let v be the combined speed of the car and truck

given that u1=35 m/sec

u2 = ?

m1 = 750 kg and m2 = 3200 kg

Using law of conservation of momentum along east -west direction

m1*u1 = (m1+m2)*V*sin(29).............(1)

along North-South direction

m2*u2 = (m1+m2)*V*cos(29)............(2)

(1)/(2)

tan(29) = (m1*u1)/(m2*u2)

tan(29) = (750*35)/(3200*u2)

u2 = 14.8 m/sec is the required speed of the truck

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