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V = 12Msqrt(gL)/5m . If you come up with this answer, the website is showing its wrong so try again please

Consider a bouncing ball. At time t = 0, the ball is dropped from a height_y(0) = họ, where ho is the initial height in meters. It falls freely. At some later time t₁ it hits the ground with a velocity y(t₁) < 0 m/s (meters per second). A bump event is produced when the ball hits the ground. The collision is inelastic (meaning that kinetic energy is lost), and the ball bounces back up with velocity −ay(t₁), where a is constant with 0 < a < 1. The ball will then rise to a certain height and fall back to the ground repeatedly. The behavior of the bouncing ball can be described by the hybrid system of Figure 1. There is only one mode, called free. When it is not in contact with the ground, we know that the ball follows the second-order differential equation, ÿ(t) = −g, where g 9.81 m/sec². = Bouncing Ball bump y(t) = 0/ bump y(t):= -ay(t) 5 free y(t) y(t)=-8 y(0) := hó y(0) := 0 Figure 1. Illustrate state variables y(t) and y(t), with initial conditions denote y(0) = ho and y (0) = 0.

Learning Goal: To apply the principle of linear impulse and momentum to a mass to determine the final speed of the mass. A 10-kg, smooth block moves to the right with a velocity of vo m/s when a force F is applied at time to = 0 s. (Figure 1) F (N) 20 10 + + t2 +r(s) 13 - 10 -20 At time to = 0s, t2 = 2.5 s, and t3 = 3.75 s. If the block is moving with an initial velocity vo = 4.75 m/s and the force remains constant at -20 N for all times greater than t3, at what time t; does the block stop moving to the right? force is applied to the block. The force varies as shown in the graph, (Figure 4), where ti = 1.25 s, Express your answer to three significant figures. • View Available Hint(s) vec ? tj = S Submit

A particle of mass m is travelling on top of a table, in a circle of radius r1, with a speed of v1. Suddenly, the attached cord is pulled down through a hole in the table, with constant speed v,. Neglect the size of the particle, the mass of the cable, and neglect friction between the particle and the table. 1) Determine a symbolic solution for the new radius r2 when the speed of the mass v2 is achieved. 2) Determine a symbolic solution for the time required for the particle to reach the speed of v2. Take time zero as the instant at which pulling on the cord begins. 3) Determine a symbolic solution for the work done on the particle between r1 and r2. 4) Numerically evaluate r2, t, and the work done on the particle for v1 = 1 ft/s, v2 = 2 ft/s, Vr 0.5 ft/s, a particle weight of 10 lb, and ri = 4 ft. The only variables that may appear in your symbolic solutions are v1, v2, Vr , m and r1.

5) A 0.5 kg ball is launched up a vertical curved circular track of radius R = 1.5 m using a spring-loaded plunger which has k = 500 N/m. The plunger keeps the spring compressed 0.08 m when s= 0. Compute the distance s the plunger must be pulled back and released so that the ball will begin to leave the track when 0-135° H k= 500 N/m 1.5 m

6) A ball is thrown vertically upward from the surface of the earth with an initial velocity of 30 m/s. Two seconds later a second ball is thrown upward from the same point with a velocity of 24 m/s. Derive an expression for the relative position, velocity, and acceleration of ball 1 with-respect-to ball 2 for time t≥2sec. (neglect air resistance and assume acceleration of gravity is 9.81 m/s2.

A 4He nucleus (atomic weight 4)moving with speed v breaks up into a neutron (atomic weight 1) anda 3He nucleus. The neutron moves off at right angles to theoriginal 4He as shown. If the neutron speed is 3v, the final speed of the 3He nucleus is (a) v. (b) √(7/3)v. (c)4v/√3. (d) √(13/3)v. (e) 5v/3.

In a free-fall experiment, an object is dropped from a height of 144 feet. A camera on the ground 500 feet from the point of impact records the fall of the object. Assuming the object is released at time t = 0. Find the rate of change of the angle of elevation of the camera when ? = 1.

Q.1 A cannon ball is fired downwards from a tower of height h = 50 m with an initial velocity of 18 m/s. Determine the velocity at which the ball hits the ground and the time it takes the ball to fall to the ground.

A 10kg object is dropped from rest from the top of a 100m cliff. Exactly one second later, an 8g bullet is fired upward from the ground with a muzzle velocity of 300(m)/(s). Assume an inelastic collision occurs between the two objects. How long after the 10kg object is dropped will the combined object hit the ground? Compare that time to the time for the 10kg object to hit the ground without the collision.

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Learning Goal: To apply the principle of linear impulse and momentum to a mass to determine the final speed of the mass. A 10-kg, smooth block moves to the right with a velocity of vo m/s when a force F is applied at time to = 0 s. (Figure 1) F (N) 20 10 +7(s) 13 12 - 10 -20 At time to = 0 s, a force is applied to the block. If the block is moving with an initial velocity vo = 2 m/s and the force varies as shown in the graph, (Figure 3), where tį = 1.25 s, t2 = 2.5 s, and t3 = 3.75 s, what is the speed of the block at time t3? Express your answer to three significant figures. • View Available Hint(s) nνα ΑΣφ It vec v(3.75 s) = m/s Submit Previous Answers

1. A chain of blocks is moving upward at 3 m/s. The tension in the cable connected to the top of the chain is T, = 800 N. a. What is the acceleration of the chain of blocks? b. What is the tension in the cable connecting Block C and Block D? v = 3 m/s ↓ g To = 800 N mA = 21 kg mB = 25 kg mc = 20 kg mp = 18 kg ME = 17 kg mF = 15 kg a = ? TCD = ?

Starting at time t = 0, net force F1 is applied to an object that is initially at rest. (a) If the force remains constant with magnitude F1 while the object moves a distance d, the final speed of the object is v1. What is the final speed v2 (in terms of v1) if the net force is F2 = 2F1 and the object moves the same distance d while the force is being applied? (b) If the force F1 remains constant while it is applied for a time T, the final speed of the object is v1. What is the final speed v2 (in terms of v1) if the applied force is F2 = 2F1 and is constant while it is applied for the same time T? In a later chapter we’ll call force times distance work and force times time impulse and associate work and impulse with the change in speed.)

At time t = 0, a projectile is launched from ground level. At t = 2.00 s, it is displaced d = 42 m horizontally and h = 59 m vertically above the launch point. What are the (a) horizontal and (b)vertical components of the initial velocity of the projectile? (c) At the instant it reaches its maximum height above ground level, what is its horizontal displacement D from the launch point?