Physics 1

A Jogger runs with constant speed \(v\) through a forest of pine trees. A pine cone starts to fall from a height \(h\) when the jogger is directly below it. How far behind the jogger will the pine cone land?
An artillery shell is fired with an initial velocity of 110 m/s at an angle of 30\(^{\circ}\) above the horizontal. Find:
- Its position and velocity after 6 s
- The time required to reach its maximum height
- The horizontal distance (range)
Determine the acceleration of the system if M = 10 kg and m = 30 kg and \(\theta\) = 30 degrees. Determine the tension in the rope as well.
A small block of mass \(M_B\) = 0.50 kg is placed on a long slab of mass \(M_S\) = 3.0 kg as shown below. Initially, the slab is at rest and the block has a speed \(v_0\) of 4.0 m/s to the right. The coefficient of kinetic friction between the block and slab is 0.20, and there is no friction between the slab and the horizontal surface on which it moves.
- Draw and label vectors to represent the forces acting on each as the block slides on the slab.
- Calculate \(v_f\) .
- Calculate the distance the slab has traveled at the moment it reaches \(v_f\) .
- Calculate the work done by friction on the slab from the beginning of its motion until it reaches \(v_f\) .
A marble, m, of mass 100 g is placed onto a platform attached to a spring. The weight of the marble compresses the spring 2 cm, as shown below. A force is then applied to the platform to compress the spring an additional 3 cm. When the force is taken away, the spring decompresses and launches the marble upward. What is the maximum height the marble obtains above the unstretched spring (the spring with no mass on it).
The mass shown below is blown apart into three pieces. Find the direction and velocity of the pink piece.
An oscillator consists of a block attached to a spring( k = 400 N/m). At some time t, the position (measured from the system's equilibrium location), velocity, and acceleration of the block are x = 0.100m, v = -13.6 m/s, and a = -123 m/s\(^2\) . Calculate the

A. frequency of oscillation

B. mass of the block

C. amplitude of the motion
A ball is thrown downward with a speed of 15 m/s from the roof of a 30 m building. At the same instant a ball is thrown upward with a speed of 15 m/s from ground level. Relative to ground level, at what height do the two balls pass each other?
A plastic ball is thrown with a velocity of 18 m/s stays in the air for 3.0 s.
- At what angle with respect to the horizontal was it released?
- What was the maximum height achieved by the ball?
Determine the acceleration of the system if M = 5 kg and m = 10 kg and \(\theta\) = 30 degrees. There is also a coefficient of friction, \(\mu\) = 0.2. Use a free body diagram to determine the tension in the rope and the acceleration of the system.

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