At what horizontal distance d from the cannon exit does the projectile land on the ground?

What is the tension in the rope when the bucket is at its lowest point assuming that its tangential velocity is vt = 6.55 m/s?

The minimum tangential speed vt of the bucket at the top of the circle is:

If the woman in the previous question doubles the constant horizontal force that she exerts on the box to push it on the same horizontal floor, the then moves:

The speed of the water, relative to the ground is:

A young girl wishes to select on of the frictionless playground slides illustrated below to give her the greatest possible speed when she reaches the bottom of the slide. Which of the slides illustrated in the diagram above should she choose?

A ball is fired by a cannon from the top of a cliff as shown in the figure below.  Which of the paths would the cannon ball most closely follow? 

When a collision is perfectly inelastic, then:

If instead she chose a heading that would get her directly across the river (point B), how long would it take her to get to the other side?

The mass of a box is 1.6 kg and the mass of the ball is 0.35 kg.  Suppose the ball has an initially horizontal velocity of 12 m/s.  What is the speed of Box 2 after the collision?