A boy stands on a shore and pulls a rope connected to a boat. The velocity of the rope v_{r} is constant. Prove that the closer the boat to the shore, the faster it moves.

# Kinematics

# A solid sphere rolls down a roof

A solid sphere starts from rest and rolls without slipping a distance of 8 m down a roof that is inclined at 25˚. The roof’s edge is 5 m high from the ground. How far horizontally from the roof’s edge does the sphere hit the ground?

# A ball is thrown vertically upwards

A ball is thrown from ground level vertically upwards with an initial velocity of v_{i}. Draw a velocity-time graph of the ball’s motion. Consider collisions with the ground are absolutely elastic and neglect air resistance.

Image By Michael Maggs Edit by Richard Bartz – Own work, CC BY-SA 3.0, Link

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# A passenger is late for a train

A passenger is late for a train. He stood at a railway station while the accelerating train passed him car by car. The passenger noticed that the last train car passed him for 8 seconds and the previous train car for 10 seconds. How long was the passenger late for the train? You should consider that the train moved with uniform acceleration and the length of the train cars is the same.

# A bomber wants to hit a target

# Shooting a bullet horizontally and dropping a bullet

# Two Stones

One stone is thrown upwards from a point on the ground with an initial velocity v_{1} and simultaneously another stone is dropped from a height. They reach the ground at the same instant. Compare the velocities which they have attained.

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