A block with mass m, = 0.500 kg is released from rest on a frictionless track at a distance h; = 2.50 m above the top of a table. It then collides elastically with an object having mass m2 = 1.00 kg that is initially at rest on the table, as shown in the figure. (a) Determine the velocities of the two objects just after the collision. (b) How high up the track does the 0.500-kg object travel back after the collision? (c) How far away from the bottom of the table does the 1.00-kg object land, given that the height of the table is h, = 2.00 m? (d) How far away from the bottom of the table does the 0.500-kg object eventually land?

You have just planted a sturdy 2-m-tall palm tree in your front lawn for your mother’s birthday. Your brother kicks a 500g ball, which hits the top of the tree at a speed of 5 m/s and stays in contact with it for 10 ms. The ball falls to the ground near the base of the tree and the recoil of the tree is minimal. (a) What is the force on the tree? (b) The length of the sturdy section of the root is only 20 cm. Furthermore, the soil around the roots is loose and we can assume that an effective force is applied at the tip of the 20 cm length. What is the effective force exerted by the end of the tip of the root to keep the tree from toppling? Assume the tree will be uprooted rather than bend. (c) What could you have done to ensure that the tree does not uproot easily?

In Figure, block A (mass 0.8 kg) slides into block B (mass 1.2 kg), along a frictionless surface.The directions of three velocities before (i) and after (f) the collision are indicated in the figure; the corresponding speeds are vAi =1.9 m/s, VBj =4.9 m/s, and ver =2.5 m/s. What are the (a) magnitude and (b) direction (left or right) of velocity Var? (c) Calculate the total kinetic energy of the system before and after the collision. Is the collision elastic?

Two titanium spheres approach each other head-on with the same speed and collide elastically. After the collision, one of the spheres, whose mass is 480 g, remains at rest. (a) What is the mass of the other sphere? (b) What is the speed of the two-sphere center of mass if the initial speed of each sphere is 4.7 m/s?

Car A and Car B are traveling in the same direction (call it i^), with B behind A, and initial speeds vA=5.6 m/s, and vB = 6 m/s. The cars have identical mass m=103 kg, and they experience an elastic collision.  Now, this collision is observed by a third person traveling in a car with constant velocity v=6 m/s, traveling in the same direction as the two cars.  From the point of view of this person calculate the following:  1)The initial momentum of car A. 2)The initial momentum of car B. 3)The final momentum of car A (you might want to first calculate the final velocity of car A relative to the ground). 4)The final momentum of car B (you might want to first calculate the final velocity of car B relative to the ground). 5)The total final kinetic energy: 6)The total final kinetic energy as measured from the ground. 7)Based on the previous answers and your calculations of the total initial kinetic energy, does the third person conclude that the collision is:

In Figure, mass m1= 2 kg with a velocity v1i =10 m/s moving in x direction makes elastic collision with m2= 4 kg that is initially at rest.(a) Find the velocity of m1 after the collision.(b) Find the velocity of m2 after the collision.(c) Find the maximum height h to which m2 rises after the collision

A 3.60-kg ball, moving to the right at a velocity of +2.35 m/s on a frictionless table, collides head-on with a stationary 10.0-kg ball. Find the final velocities of (a) the 3.60-kg ball and of (b) the 10.0-kg ball if the collision is elastic. (c) Find the magnitude and direction of the final velocity of the two balls if the collision is completely inelastic.

A pendulum of length L = 0.98 m hangs at rest with  2.0 kg bob. The string is of negligible mass.  A smaller 0.10 kg mass is traveling to the left at 20.0 m/s and has an elastic collision with the pendulum bob. Assume that positive is to the right. a) What is the velocity of the bob immediately after the elastic collision?

Two balls of masses m, = 3.90 kg and m, = 1.60 kg move along the x axis. The initial velocities of the balls are VLj = 28.0 m/s and v2j = -12.0 m/s. The balls collide in a head-on elastic collision. Find the velocities of the balls after the collision. (a) First ball: V1,f m/s (b) Second ball:. V2,f = m/s

In Figure, block A (mass 0.8 kg) slides into block B (mass 1.2 kg), along a frictionless surface.The directions of three velocities before (i) and after (f) the collision are indicated in the figure; the corresponding speeds are vAi =1.9 m/s, vâi =4.9 m/s, and vBr=2.5 m/s.What are the (a) magnitude and (b) direction (left or right) of velocity var? (c) Calculate the total kinetic energy of the system before and after the collision. Is the collision elastic? VA = ?