A 2.06-kg particle has a velocity (1.92 î − 2.98 ĵ) m/s, and a 2.90-kg particle has a velocity (1.06 î + 5.93 ĵ) m/s. (a) Find the velocity of the center of mass. (b) Find the total momentum of the system.

Two people, each with a mass of 85.00 kg, are paddling their canoe downstream with a speed of 1.520 m/s relative to the water, in a river that flows with a speed of 2.790 m/s with respect to the shore. What is the magnitude of the total momentum of the people, in kg⋅m/s, with respect to the shore?

A 0.0210 kg bullet moving horizontally at 450 m/s embeds itself into an initially stationary 0.500 kg block. (a) What is their velocity (in m/s) just after the collision? m/s (b) The bullet-embedded block slides 8.0 m on a horizontal surface with a 0.30 kinetic coefficient of friction. Now what is its velocity (in m/s)? m/s (c) The bullet-embedded block now strikes and sticks to a stationary 2.00 kg block. How far (in m) does this combination travel before stopping? m

A particle with an initial linear momentum of 2.30 kg · m/s directed along the positive x-axis collides with a second particle, which has an initial linear momentum of 4.60 kg · m/s, directed along the positive y-axis. The final momentum of the first particle is 3.45 kg · m/s, directed 45.0° above the positive x-axis. Find the final momentum of the second particle. magnitude   direction above the negative x-axis

A 1.95-kg particle has a velocity (1.95 î – 3.07 ĵ) m/s, and a 2.91-kg particle has a velocity (1.06 î + 5.99 ĵ) m/s. (a) Find the velocity of the center of mass. i) m/s (b) Find the total momentum of the system. |î) kg · m/s

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 system of three particles with masses m1 = 3.0 kg, m2 = 4.0 kg and m3 = 8.0 kg is placed on a two dimensional xy plane. The scales on the axes are set by x, = 2.0 m and y, = 2.0 m. y (m) mg m1 * (m) Figure 2 (a) Find out the x coordinate of the system's center of mass. (b) Find out the y coordinate of the system's center of mass. (c) Find out the acceleration of the system if an external force of 5 N acts on it.

Two carts mounted on an air track are moving toward one another. Cart 1 has a speed of 0.9 m/s and a mass of 0.53 kg. Cart 2 has a mass of 0.75 kg. (a) If the total momentum of the system is to be zero, what is the initial speed (in m/s) of Cart 2? (Enter a number.) ?m/s (b) Does it follow that the kinetic energy of the system is also zero since the momentum of the system is zero? Yes or No     (c) Determine the system's kinetic energy (in J) in order to substantiate your answer to part (b). (Enter a number.) J

A 0.346 kg puck, initially at rest on a hor- izontal, frictionless surface, is struck by a 0.275 kg puck moving initially along the r axis with a speed of 2.01 m/s. After the colli- sion, the 0.275 kg puck has a speed of 1.01 m/s at an angle of 37° to the positive x axis. Determine the magnitude of the velocity of the 0.346 kg puck after the collision. Answer in units of m/s. Answer in units of m/s. 1. 1.3422 2. 1.21901 3. 0.347028 4. 1.14264 5. 1.07153 6. 0.637653 7. 0.328271 8. 0.591588 9. 0.551494 10. 1.00165

A system of four particles moves along one dimension. The center of mass of the system is at rest, and the particles do not interact with any objects outside of the system. Find the velocity v4 of particle 4 at t1 = 2.75 s given the details for the motion of particles 1, 2, and 3. particle 1: mj = 1.33 kg, vi (t) = (7.41 m/s) + (0.277 m/s²) × t particle 2: m2 = 3.05 kg, v2 (t) = (8.05 m/s) + (0.567 m/s²) × t particle 3: m3 = 4.25 kg, v3 (t) = (6.33 m/s) + (0.195 m/s²) × t particle 4: m4 = 5.27 kg