A small block of mass m, = 0.855 kg is released from rest at the top of a curved wedge of mass m, = 8.80 kg, which sits on a frictionless horizontal surface as in figure (a). When the block leaves the wedge, its velocity is measured to be 4.00 m/s to the right, as in figure (b).

A cannon of mass 6.79 x 103 kg is rigidly bolted to the earth so it can recoil only by a negligible amount. The cannon fires a 85.6-kg shell horizontally with an initial velocity of 508 m/s. Suppose the cannon is then unbolted from the earth, and no external force hinders its recoil. What would be the velocity of a shell fired from this loose cannon? (Hint: In both cases assume that the burning gunpowder imparts the same kinetic energy to the system.)

An astronaut in her space suit has a total mass of m1 = 79.5 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 = 8.50 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 2.20 min (the amount of time the air in her helmet remains breathable).m

An astronaut in her space suit has a total mass of  m1 = 78.5 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 = 8.50 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.

A rocket, which is in deep space and initially at rest relative to an inertial reference frame, has a mass of 86.2 × 105 kg, of which 14.7 × 105 kg is fuel. The rocket engine is then fired for 180 s, during which fuel is consumed at the rate of 480 kg/s. The speed of the exhaust products relative to the rocket is 2.98 km/s. (a) What is the rocket's thrust? After the 180 s firing, what are (b) the mass and (c) the speed of the rocket?

A rocket, which is in deep space and initially at rest relative to an inertial reference frame, has a mass of 75.8 x 105 kg, of which 15.3 × 105 kg is fuel. The rocket engine is then fired for 410 s, during which fuel is consumed at the rate of 390 kg/s. The speed of the exhaust products relative to the rocket is 2.81 km/s. (a) What is the rocket's thrust? After the 410 s firing, what are (b) the mass and (c) the speed of the rocket? (a) Number i Units (b) Number i Units (c) Number i Units

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 baseball of mass m1 = 0.27 kg is thrown at another ball hanging from the ceiling by a length of string L = 1.05 m. The second ball m2 = 0.77 kg is initially at rest while the baseball has an initial horizontal velocity of V1 = 3.5 m/s. After the collision the first baseball falls straight down (no horizontal velocity). (a) Select an expression for the magnitude of the closest distance from the ceiling the second ball will reach d. (b) What is the angle that the string makes with the vertical at the highest point of travel in degrees?

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?

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).