An explosive device of mass m lies at rest on an inclined plane that makes an angle with respect to the horizontal. At some instant, the explosive detonates and separates into two pieces. One piece of mass m₁ begins to travel horizontally with speed v₁, while the other piece travels up along the ramp. What is the initial speed of the second piece just after the explosion?
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- Two spheres collide on a horizontal surface (all velocities, before and after the collision, are in the x-y plane). Throughout this problem, assume that all forces aside from those exerted by the spheres themselves are negligible (at least in comparison). Sphere A has a mass of 0.65 grams. It has an initial speed of 6.0 m/s and an initial velocity that is oriented at an angle of θ A i = 28 degrees below the x-axis. Sphere B has a mass of 0.45 grams. It has an initial speed of 6.5 m/s and an initial velocity that is oriented at an angle of θ B i = 35 degrees above the x-axis. After the collision, sphere A has a speed of 3.5 m/s and a velocity that is directed at an angle of θ A f = 16 degrees above the x-axis. What is the final speed, in units of meters per second, of sphere B?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.In the figure, two particles are launched from the origin of the coordinate system at time t - O. Particle 1 of mass m₁ - 5.20 g is shot directly along the x axis (on a frictionless floor), where it moves with a constant speed of 10.7 m/s. Particle 2 of mass m₂ -4.50 g is shot with a velocity of magnitude 15.6 m/s, at an upward angle such that it always stays directly above particle 1 during its flight. (a) What is the maximum height Hmax reached by the com of the two-particle system? In unit-vector notation, what are the (b) velocity and (c) acceleration of the com when the com reaches Hmax? (a) Number 3.05 (b) Number 10.7 (c) Number 0 Units i+ 0 m 3.3 j Units m/s j Units m/s^2
- A firework with mass M is launched from the origin with initial speed v0 and angle θ0 and travels along the usual parabolic path above flat ground. At the peak of its path, it explodes into two pieces. Piece one has mass .5M and speed v1 in an angle of 30◦ below the horizontal direction and the other piece has mass .5M and speed v2 in an unknown direction. (a) Do the two pieces land at the same time? (Justify your answer) (b) Sketch the motion of the COM and of both pieces. Note any external forces, and describe if p is conserved in x, y or both for the duration of the flight. Also note if the two pieces land at the same distance from the target or describe which one lands closer/further.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?A rocket ship is travelling through space. The fuselage section has a mass of 505 kg. The Nose Cone (front end) section has a mass of 100 kg. The rocket is travelling at 52.0 m/s when the rocket engine stops and the two sections are separated by an explosion in such a way that they stay in a straight line. If the Nose Cone section (front end) continues forward at 98.0 m/s, determine the speed of the Fuselage section after the separation.
- 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 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 UnitsA 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
- An astronaut finds herself in a predicament in which she has become untethered from her shuttle. She figures that she could get back to her shuttle by throwing one of three objects she possesses in the opposite direction of the shuttle. The masses of the objects are 5.4 kg, 7.9 kg, and 10.1 kg, respectively. She is able to throw the first object with a speed of 15.00 m/s, the second with a speed of 14.2 m/s, and the third with a speed of 7.0 m/s. If the mass of the astronaut and her remaining gear is 75.0 kg, determine the final speed of the astronaut with respect to the shuttle if she were to throw each object successively, starting with the least massive and ending with the most massive. Assume that the speeds described are those measured in the rest frame of the astronaut.You throw up a basketball vertically into the air, and your friend shoots an arrow horizontally with speed vi at top of the basketball's trajectory where it momentarily comes to rest. The arrow passes through center-of-mass of the ball. Assuming the collision takes place over a short time ∆t, what is the average force of the arrow on the ball during the collision, expressed in terms of m (mass arrow), M (mass ball), ∆t, and vi ?An instrument-carrying projectile of mass m1 accidentally explodes at the top of its trajectory. The horizontal distance between launch point and the explosion is x0. The projectile breaks into two pieces that fly apart horizontally. The larger piece, m3, has three times the mass of the smaller piece, m2. To the surprise of the scientist in charge, the smaller piece returns to earth at the launching station. Neglect air resistance and effects due to the earth’s curvature. How far away from the original launching point does the larger piece land