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- 2. A 40 kg astronaut is floating in space, initially motionless in the reference frame of her nearby space ship. She has in her possession two 5 kg oxygen canisters. She suddenly notices a small 4 kg asteroid heading straight for her at a speed of 5 m/s. Wanting to avoid a collision she hurls one of the two canisters as hard as she can (3 m/s relative to her frame just before the throw) at the asteroid. The canister hits the asteroid dead on and sticks to it. A) After she throws the canister, what is her velocity relative to the space ship? B) After the canister sticks to the asteroid, what is the asteroid's velocity relative to the ship? C) She then hurls the second canister as hard as she can (3 m/s relative to her frame just before the throw), which again hits the asteroid dead on and sticks to it. What is her velocity relative to the space ship now? D) What is the asteroid's velocity now relative to the ship? Have her actions managed to avoid an impending collision between her and…M of its initial mass to ME 3 A spaceship's orbital maneuver requires a speed increase of 1.05 x 10° m/s. If its engine has an exhaust speed of 2.85 x 10° m/s, determine the required ratio its final mass. (The difference M, - M, equals the mass of the ejected fuel.) HINT Need Help? Watch It Read ItFor years, the tallest tower in the United States was the Phoenix Shot Tower in Baltimore, Maryland. The shot tower was used from 1828 to1892 to make lead shot for pistols and rifles and molded shot for cannons and other instruments of warfare. Molten lead was dropped from the top of the 82.15 m tall tower into a vat of water. During its free fall, the lead would form a perfectly spherical droplet and solidify. Determine the velocity of the droplet right before it hits the ground. (Note: acceleration = -9.81 m/s/s) (Hint: think about the direction the droplet travels when considering its displacement.) ___________m/s
- 1. An electric rocket is to be designed to provide a Aub of 5.7 km/s. Given that the "burn" time is 3 months, and (an) is 10 kg/kW, calculate the optimum specific impulse, and the corresponding (ML/Mo). Show table of values of (ML/Mo) and Isp that supports your conclusion and highlight the necessary information in it. It is sufficient to provide the portion of the table around the highlighted region. {Ans.: 3700s, 0.7316}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?1. Show that in the CM frame of two particles, the angular momentum // of particle 1 is related to the total angular momentum L by 1 (m₂/M) L and likewise 12-(m₁/M) L.
- An 8.24 kg mass moving east at 17.2 m/s on a frictionless horizontal surface collides with a 11.4 kg mass that is initially at rest. After the collision, the 8.24 kq mass moves south at 2.06 m/s. What is the magnitude of the velocity of the 11.4 kg mass after the collision? Submit Answer Tries 0/90 What is the angle relative to the east? Submit Answer Tries 0/90 What percentage of the initial kinetic energy is lost in the collision? Do not enter units. Submit Answer Tries 0/90C4B.1 Consider a system consisting of two point particles A and B separated by 25 cm. The distance between particle A and the system's center of mass is 5 cm. What is the mass of particle B compared to the mass of particle A? (Hint: Put the center of mass at the origin.)Two stars in a binary system orbit around their center of mass. The centers of the two stars are 7.49x10¹¹ m apart. The larger of the two stars has a mass of 4.15x10³0 kg, and its center is 2.38x10¹¹ m from the system's center of mass. What is the mass of the smaller star?
- 25. Suppose a cart with mass m and low-friction wheels is moving to the right at an initial speed of v just before it hits a cart with mass 2m. After the collision, the first cart rebounds to the left with a speed of Assume each cart receives zero net momentum from any external interactions (such as gravitational and contact interactions) other than their collision interaction. (a) What impulses did the collision interaction deliver to each cart? Express the impulses' directions as "left" or "right" and their magnitudes as multiples of m right ward or e tward lett war The impulse delivered to the light cart is mvo(Click to select) vol (Click to select) . htunrd or The impulse delivered to the massive cart is m|vo (b) From this, Infer the massive cart's final velocity v (express its magnitude in terms of o and its direction as being "left" or "right"). nighturrd or leftward The massive cart's velocity is oll(Click to select) Hints Hint H14 p An explosion breaks an object, originally at rest, into two fragments. Fragment 1 has mass mi and acquires twice the kinetic energy of fragment 2 with mass m2. What is the ratio of their masses? (A) m1/m2 = } %3D (B) m1/m2 = } (C) m1/m2 = } (D) mı/m2 = 1 (E) m1/m2 = 2 (F) m1/m2 = 3 G) m1/m2 = 42. A 'small' asteroid with a mass of 1000kg is moving through deep space with a constant velocity of 30 m/s. Suddenly the small asteroid collides with a large asteroid possessing a mass of 10,000kg. The large asteroid was initially at rest and the collision causes the small mass to become completely embedded within the larger one so that they are now one combined mass. a. What is the speed of the combined mass system after the collision? b. How many Joules of energy were lost due to the collision?